The value of $\tan ^{-1}(-\sqrt{3})+\cos ^{-1}\left(-\frac{1}{2}\right)$ is:

$\frac{\pi}{3}$ $-\frac{\pi}{3}$ $\frac{2 \pi}{3}$ $\pi$

$\frac{\pi}{3}$

The correct answer is Option (1) → $\frac{\pi}{3}$