For every angle θ, sin(540° − θ) equals:

540° = 360° + 180°, and the sine repeats every 360°, so sin(540° − θ) = sin(180° − θ) = sinθ. Check at θ = 30°: sin510° = sin150° = 1/2 = sin30°. Treating 540° as an odd multiple of 90° instead would wrongly turn the sine into a cosine.