Remark
You are in the 4th quadrant. The only way I know how to do this is to use the double angle formula.
Formula
Sin(a + b) = sin(a) * cos(b) + sin(b)*cos(a)
Givens
a = - 45
b = - 30
Substitute
Sin(-45 - 30) = sin(-45) * cos(-30) + sin(-30)*cos(-45)
Sin(-75) = -sqrt(2)/2*sqrt(3)/2 - 1/2 * sqrt(2)/2
Sin(-75) = -sqrt(6) / 4 - sqrt(2)/4
Sin(-75) = [tex] \frac{-\sqrt{6}- \sqrt{2} }{4} [/tex]
