Find the principal value of each of the following :

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

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

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