Answer
$\dfrac{-\pi}{3}$
Work Step by Step
We know that if $\tan{(y)}=x$, then $\tan^{-1}{x}=y.$
Since $\tan{(-\frac{\pi}{3})}=-\sqrt3$, then by the definition of the inverse function:
$\tan^{-1}(-\sqrt3)=\frac{-\pi}{3}$. (because it is in the right domain)