Answer
$x = 0, ~~\frac{\pi}{3},~~\pi, ~~\frac{5\pi}{3}, ~~2\pi$
Work Step by Step
$sin~2x = sin~x$
$2~sin~x~cos~x = sin~x$
Case 1: $sin~x = 0$
$x = 0, \pi, 2\pi$
Case 2: $sin~x \neq 0$
$2~sin~x~cos~x = sin~x$
$2~cos~x = 1$
$cos~x = \frac{1}{2}$
$x = \frac{\pi}{3}, \frac{5\pi}{3}$