ArcSin[(-1)^(1/4)/2^(3/4)] == Pi/8 + (1/2)*I*Log[1 + Sqrt[2]] (Compute just the real part?) Pi/2 == ArcSin[13/85] + ArcSin[5/13] + ArcSin[8/17] + ArcSin[33/65] (Obviously inferior to ArcSin[1/2].) Pi/2 == ArcSin[73/2665] + ArcSin[21/221] + ArcSin[13/85] + ArcSin[9/41] + ArcSin[7/25] + 2*ArcSin[5/13] Pi/2 == 4*ArcSin[191/18241] + 20*ArcSin[187/17485] - 4*ArcSin[157/12325] + 9*ArcSin[99/4901] + 8*ArcSin[93/4325] + 20*ArcSin[164/6725] + 8*ArcSin[160/6401] - ArcSin[140/4901] + 12*ArcSin[136/4625] --rwg asin(x)*asin(y) = sqrt(%pi)* inf ==== 2 2 2(n + 1) 2(n + 1) 2(n + 1) \ n! ((x sqrt(1-y ) + sqrt(1-x ) y) - y - x ) > ------------------------------------------------------------------ / 1 ==== 4 (n + 1) (n + -)! n = 0 2