比较大小: $\tan \left(-\frac{2 \pi}{7}\right)$ $\tan \left(-\frac{\pi}{5}\right)$.
$\tan \left(-\frac{2 \pi}{7}\right)=\tan \frac{5 \pi}{7}, \tan \left(-\frac{\pi}{5}\right)=\tan \frac{4 \pi}{5}$,

又 $y=\tan x$ 在 $\left(\frac{\pi}{2}, \pi\right)$ 内单调递增,

所以 $\tan \frac{5 \pi}{7}<\tan \frac{4 \pi}{5}$,

即 $\tan \left(-\frac{2 \pi}{7}\right)<\tan \left(-\frac{\pi}{5}\right)$.