sin ( arcsin (1/2) + arrcos(2/3) )
arcsin (1/2) = A
So
sin A = 1/2 and cos A = sqrt ( 2^2 - 1^2) / 2 = sqrt (3) / 2
arccos (2/3) = B
So
cos B = (2/3) and sin B = sqrt ( 3^2 - 2^2) / 3 = sqrt (5) /3
sin (A + B) =
sin Acos B + sin B cos A =
(1/2)(2/3) + (sqrt (5) / 3) (sqrt (3) / 2) =
[ 2 + sqrt (15) ] / 6