Answer
$\frac{\pi}{6}.$
Work Step by Step
The domain of $\tan^{-1}{x}$ is the range of $\tan{x}$, which is the real numbers.
The range of $\tan^{-1}{x}$ is a specified domain of $\tan{x}$, i.e. $\left(− \frac{\pi}{2} , \frac{\pi}{2} \right)$.
We know that if $\tan y=x$, then $\tan^{-1}(x)=y.$
We know that $\tan(\frac{\pi}{6})=\frac{\sqrt3}{3}$, hence $\tan^{-1}(\frac{\sqrt3}{3})=\frac{\pi}{6}.$
