# How do you evaluate arctan(-sqrt3/3) without a calculator?

$- \frac{\pi}{6}$
${\tan}^{-} 1 \left(- \frac{\sqrt{3}}{3}\right) = - \frac{\pi}{6}$.Since $\tan \left(- \frac{\pi}{6}\right) = - \frac{\sqrt{3}}{3}$ and $- \frac{\pi}{6} \in \left(- \frac{\pi}{2} , \frac{\pi}{2}\right)$[Ans]