Trigonometric Equations · Medium problem

A student solves $\sin x = \sin x\cos x$ on $[0, 2\pi)$ by dividing both sides by $\sin x$. This gives $\cos x = 1$, so the student reports the single solution $x = 0$. The equation has exactly one other solution in $[0, 2\pi)$ that the division lost. Find it.