Answer
$-\dfrac{\pi}{3}$
Work Step by Step
We need to find $\tan^{-1} (-\sqrt 3). $
The inverse tangent function has the range $-\dfrac{\pi}{2} \leq \theta \leq \dfrac{\pi}{2}$. We are looking for the angle whose tangent value equals $-\sqrt 3$.
Since, $-\dfrac{\pi}{3}$ lies in $-\dfrac{\pi}{2} \leq \theta \leq \dfrac{\pi}{2}$, then we have:
$\tan^{-1} (-\sqrt 3) =-\dfrac{\pi}{3}$
