Solve for all radian solutions and x if 0 sin x + 2sin x cos x=0

the answer is

sin x + 2sin x cos x=0

sin x (1 + 2 cos x) = 0, so sin x = 0 or (1 + 2 cos x) = 0, implies cos x = - 1/2

the solutions are x = arc sin 0 = 2Pi + 2kpi or x=arccos (-1/2) = 2Pi/3 + 2kpi