已知 $M=\left\{x \left\lvert\,-\frac{1}{2} \leqslant \sin x \leqslant \frac{1}{2}\right.\right\}, N=\left\{-\frac{\pi}{4},-\frac{\pi}{6}, 0, \frac{\pi}{3}\right\}$, 则 $M \cap N=$
A. $\left\{-\frac{\pi}{6}, 0\right\}$
B. $\left\{-\frac{\pi}{4}, 0\right\}$
C. $\left\{-\frac{\pi}{6}, 0, \frac{\pi}{3}\right\}$
D. $\left\{-\frac{\pi}{4},-\frac{\pi}{6}, 0\right\}$