eqns =
(6139717614991987*sin(alpha1 - 5260496593329511/4503599627370496))/576460752303423488 - (6139717614991987*sin(alpha1 + 8887978910727369/4503599627370496))/576460752303423488 - (6139717614991987*sin(alpha1 - alpha2 + 2426121512173299/562949953421312))/576460752303423488 + (6139717614991987*sin(alpha2 + 1315124148332377/1125899906842624))/576460752303423488 - (6838973222433983*sin(alpha1 - alpha3 + 7013387595735251/576460752303423488))/4611686018427387904 + (6838973222433983*sin(alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 == 0
(6139717614991987*sin(alpha1 - 5260496593329511/4503599627370496))/576460752303423488 + (6139717614991987*sin(alpha2 + 1315124148332377/1125899906842624))/576460752303423488 - (6116011302834163*sin(alpha1 - alpha2 + 5262616901442313/4503599627370496))/576460752303423488 - (8613863080971509*sin(alpha2 - 6441676431083497/9007199254740992))/576460752303423488 + (6838973222433983*sin(alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 + (3832166839221645*sin(alpha3 - alpha2 + 8439790959623567/18014398509481984))/2305843009213693952 == 0
(6139717614991987*sin(alpha1 - 5260496593329511/4503599627370496))/576460752303423488 + (6139717614991987*sin(alpha2 + 1315124148332377/1125899906842624))/576460752303423488 - (6838973222433983*sin(alpha1 - alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 - (6838973222433983*sin(alpha2 - alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 - (6838973222433983*sin(alpha3 + 7013387595735251/576460752303423488))/4611686018427387904 + (6838973222433983*sin(alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 + 6183203739346277/18446744073709551616 == 0
(6139717614991987*sin(alpha1 - 5260496593329511/4503599627370496))/576460752303423488 - (6139717614991987*sin(alpha1 + 8887978910727369/4503599627370496))/576460752303423488 - (6139717614991987*sin(alpha1 - alpha2 + 2426121512173299/562949953421312))/576460752303423488 + (6139717614991987*sin(alpha2 + 1315124148332377/1125899906842624))/576460752303423488 - (6838973222433983*sin(alpha1 - alpha3 + 7013387595735251/576460752303423488))/4611686018427387904 + (6838973222433983*sin(alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 == 0
(6139717614991987*sin(alpha1 - 5260496593329511/4503599627370496))/576460752303423488 + (6139717614991987*sin(alpha2 + 1315124148332377/1125899906842624))/576460752303423488 - (6116011302834163*sin(alpha1 - alpha2 + 5262616901442313/4503599627370496))/576460752303423488 - (8613863080971509*sin(alpha2 - 6441676431083497/9007199254740992))/576460752303423488 + (6838973222433983*sin(alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 + (3832166839221645*sin(alpha3 - alpha2 + 8439790959623567/18014398509481984))/2305843009213693952 == 0
(6139717614991987*sin(alpha1 - 5260496593329511/4503599627370496))/576460752303423488 + (6139717614991987*sin(alpha2 + 1315124148332377/1125899906842624))/576460752303423488 - (6838973222433983*sin(alpha1 - alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 - (6838973222433983*sin(alpha2 - alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 - (6838973222433983*sin(alpha3 + 7013387595735251/576460752303423488))/4611686018427387904 + (6838973222433983*sin(alpha3 + 7046841706732599/2251799813685248))/4611686018427387904 + 6183203739346277/18446744073709551616 == 0