Answer
$\frac{2\pi}{3}$
Work Step by Step
We know that $\cot \frac{\pi}{3}=\frac{1}{\sqrt 3}$
$⇒ -\cot \frac{\pi}{3}= -\frac{1}{\sqrt 3}$
$⇒\cot(\pi-\frac{\pi}{3})=-\frac{1}{\sqrt 3}$
$⇒\cot(\frac{2\pi}{3})=- \frac{1}{\sqrt 3}$
Thus we get,
$\cot^{-1}(-\frac{1}{\sqrt 3})= \frac{2\pi}{3}$
