设集合 $\mathbf{M}=\left\{\alpha \left\lvert\, \alpha=\frac{k \pi}{2}-\frac{\pi}{3}\right., k \in Z\right\}, \mathbf{N}=\{\boldsymbol{\alpha} \mid-\pi<\boldsymbol{\alpha}<\pi\}$, 则 $\mathbf{M} \cap \mathbf{N}=$
由 $-\pi<\frac{k \pi}{2}-\frac{\pi}{3}<\pi$, 得 $-\frac{4}{3}<\mathrm{k}<\frac{8}{3}, \because \mathrm{k} \in \mathrm{Z}$,

$\therefore \mathrm{k}=-1,0,1,2$, 故 $\mathrm{M} \cap \mathrm{N}=\left\{-\frac{5}{6} \pi,-\frac{\pi}{3}, \frac{\pi}{6}, \frac{2}{3} \pi\right\}$