sin x = - 1/4, x=(-1)^n arcsin (-1\4) + \pi n = (-1)^{n+1} arcsin 1/4

(asin(-0.25))

subtract from 360 an absolute value of this angle and you get a positive number (I guess you're aware that **"- angle**" means way clockwise from the 0 grades point on the 360 grades circle) that is identical to the found root of the equation.