Решите систему неравенств

Решите задачу:

$\left \{ {{sinx \leq 0} \atop {sinx\ \textgreater \ -\frac{\sqrt3}{2}}} \right. \; \left \{ {{-\pi +2\pi n \leq x \leq 2\pi n\; ,\; n\in Z} \atop {-\frac{\pi}{3}+2\pi k\ \textless \ x\ \textless \ \frac{4\pi}{3}+2\pi k\; ,\; k\in Z}} \right. \\\\x\in (-\frac{\pi}{3}+2\pi n;2\pi n]\cup [\, \pi +2\pi n;\frac{4\pi}{3}+2\pi n)$