Solution
= Solution
In one period, <sine> equals $-\sqrt3/2$ at $4\pi/3$ and $5\pi/3$, and lies below that value between them. Since <sine> is a <periodic function> with period $2\pi$, all solutions are:
$$
\boxed{x\in\bigcup_{k\in\mathbb Z}\left[\frac{4\pi}{3}+2\pi k,\ \frac{5\pi}{3}+2\pi k\right].}
$$
The endpoints are included because the inequality is non-strict.