Вычислить: arctg (tg 10pi/13)

Решите задачу:

$arctg(tg\frac{10\pi}{13})=?\\\\\frac{\pi}{2}\ \textless \ \frac{10\pi}{13}\ \textless \ \pi\; \; \Rightarrow \; \; \frac{10\pi}{13}=\pi -\frac{3\pi}{13}\\\\tg\frac{10\pi}{13}=tg(\pi -\frac{3\pi}{13})=tg(-\frac{3\pi}{13})\; ,\; \frac{\pi}{2}\ \textless \ -\frac{3\pi}{13}\ \textless \ \frac{\pi}{2}\\\\arctg(tg \alpha )= \alpha \; ,\; esli\; \; -\frac{\pi}{2}\ \textless \ \alpha \ \textless \ \frac{\pi}{2}\; .\\\\arctg(tg\frac{10\pi}{13})=arctg(tg(-\frac{3\pi}{13}))=-\frac{3\pi}{13}$