Find the principal value of each of the following :

$\sec ^{-1}\left(\frac{-2}{\sqrt{3}}\right)=\pi-\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)\left[\right.$ Formula: $\left.\sec ^{-1}(-x)=\pi-\sec ^{-1}(x)\right]$

$=\pi-\frac{\pi}{6}$

$=\frac{5 \pi}{6}$