😊出会いの泉😊

tanの加法定理で計算していくだけですが、かなり長いです。
x=-arctan(1/88942800178226109582168404411725)
+arctan(1/61775097240445660329693394511093237957733203657982660526882)
とおくと
tan(x)={tan(-arctan(1/88942800178226109582168404411725))
+tan(arctan(1/61775097240445660329693394511093237957733203657982660526882))}
/{1-tan(-arctan(1/88942800178226109582168404411725))
*tan(arctan(1/61775097240445660329693394511093237957733203657982660526882))}
=(-1/88942800178226109582168404411725
+1/61775097240445660329693394511093237957733203657982660526882)
/(1+1/88942800178226109582168404411725
*1/61775097240445660329693394511093237957733203657982660526882)
=-9489/843978230891187553825195990678004927
なので
-arctan(1/88942800178226109582168404411725)
+arctan(1/61775097240445660329693394511093237957733203657982660526882)
=-arctan(9489/843978230891187553825195990678004927)

x=-arctan(1/54838715017299308)-arctan(9489/843978230891187553825195990678004927)
とおくと
tan(x)={tan(-arctan(1/54838715017299308))
+tan(-arctan(9489/843978230891187553825195990678004927))}
/{1-tan(-arctan(1/54838715017299308))
*tan(-arctan(9489/843978230891187553825195990678004927))}
=(-1/54838715017299308-9489/843978230891187553825195990678004927)
/(1-1/54838715017299308*9489/843978230891187553825195990678004927)
=-377467/20699805241434905130131
なので
-arctan(1/54838715017299308)-arctan(9489/843978230891187553825195990678004927)
=-arctan(377467/20699805241434905130131)

x=-arctan(1/99368343)-arctan(377467/20699805241434905130131)
とおくと
tan(x)={tan(-arctan(1/99368343))+tan(-arctan(377467/20699805241434905130131))}
/{1-tan(-arctan(1/99368343))*tan(-arctan(377467/20699805241434905130131))}
=(-1/99368343-377467/20699805241434905130131)
/(1-1/99368343*377467/20699805241434905130131)
=-1519876048/151027564181484889
なので
-arctan(1/99368343)-arctan(377467/20699805241434905130131)
=-arctan(1519876048/151027564181484889)

x=arctan(1/142057)-arctan(1519876048/151027564181484889)
とおくと
tan(x)={tan(arctan(1/142057))+tan(-arctan(1519876048/151027564181484889))}
/{1-tan(arctan(1/142057))*tan(-arctan(1519876048/151027564181484889))}
=(1/142057-1519876048/151027564181484889)/(1+1/142057*1519876048/151027564181484889)
=1466625710157/208642724182192949
なので
arctan(1/142057)-arctan(1519876048/151027564181484889)
=arctan(1466625710157/208642724182192949)

x=arctan(1466625710157/208642724182192949)
とおくと
tan(2x)=2tan(arctan(1466625710157/208642724182192949))
/{1-(tan(arctan(1466625710157/208642724182192949)))^2}
=(2*1466625710157/208642724182192949)/{1-(1466625710157/208642724182192949)^2}
=306000783522799810880723082993/21765893176007825702703449046175976
なので
2arctan(1466625710157/208642724182192949)
=arctan(306000783522799810880723082993/21765893176007825702703449046175976)

x=arctan(1/275807)
+arctan(306000783522799810880723082993/21765893176007825702703449046175976)
とおくと
tan(x)={tan(arctan(1/275807))
+tan(arctan(306000783522799810880723082993/21765893176007825702703449046175976))}/{1-tan(arctan(1/275807))
*tan(arctan(306000783522799810880723082993/21765893176007825702703449046175976))}
=(1/275807+306000783522799810880723082993/21765893176007825702703449046175976)
/(1-1/275807*306000783522799810880723082993/21765893176007825702703449046175976)=1744507482180328366854565127/98646395734210062276153190241239
なので
arctan(1/275807)
+arctan(306000783522799810880723082993/21765893176007825702703449046175976)
=arctan(1744507482180328366854565127/98646395734210062276153190241239)

x=arctan(1/28)
とおくと
2x=arctan(2(1/28)/(1-(1/28)^2))=arctan(56/783)
4x=arctan(2(56/783)/(1-(56/783)^2))=arctan(87696/609953)
5x=arctan((87696/609953+1/28)/(1-87696/609953*1/28))=arctan(3065441/16990988)
10x=arctan(2(3065441/16990988)/(1-(3065441/16990988)^2))
=arctan(104169742491416/279296744691663)
11x=arctan((104169742491416/279296744691663+1/28)/(1-104169742491416/279296744691663*1/28))
=arctan(3196049534451311/7716139108875148)
22x=arctan(2(3196049534451311/7716139108875148)/(1-(3196049534451311/7716139108875148)^2))
=arctan(49322325613363940973893167838056/49324070120846121302260022403183)
よって
22arctan(1/28)=arctan(49322325613363940973893167838056/49324070120846121302260022403183)

そして
x=arctan(49322325613363940973893167838056/49324070120846121302260022403183)
+arctan(1744507482180328366854565127/98646395734210062276153190241239)
とおくと
tan(x)={tan(arctan(49322325613363940973893167838056/49324070120846121302260022403183))
+tan(arctan(1744507482180328366854565127/98646395734210062276153190241239))}
/{1-tan(arctan(49322325613363940973893167838056/49324070120846121302260022403183))
*tan(arctan(1744507482180328366854565127/98646395734210062276153190241239))}
=(49322325613363940973893167838056/49324070120846121302260022403183
+1744507482180328366854565127/98646395734210062276153190241239)
/(1-49322325613363940973893167838056/49324070120846121302260022403183
*1744507482180328366854565127/98646395734210062276153190241239)
=1
なので
arctan(49322325613363940973893167838056/49324070120846121302260022403183)
+arctan(1744507482180328366854565127/98646395734210062276153190241239)
=arctan(1)
=π/4

らすかるさん、大変ありがとうございました。