sin(a+45)=-pi/4 expand using formula sina+cosa=-pi/4*2^1/2 squaring sin2a=pi^2/8 - 1 now writing sin2a as 2 sina cosa and then cosa as root of 1-sin^2a we get fourth degree eqn in sina solving which we get sina =root of (8+ or - pi root of 16-pi^2)/16