If $\tan^{-1} x = -\frac{\pi}{3}$, what is $x$?

Explanation

1. 01

   $x = \tan\left(-\frac{\pi}{3}\right)$, and $-\frac{\pi}{3}$ is on the branch.

2. 02

   $\tan\left(-\frac{\pi}{3}\right) = -\sqrt{3}$.