What is the value of $\cos^{-1}\left(\frac{1}{2}\right) + 2\sin^{-1}\left(\frac{1}{2}\right)$?

Explanation

1. 01

   Take each principal value on its own branch.

2. 02

   $\frac{\pi}{3} + 2 \times \frac{\pi}{6} = \frac{2\pi}{3}$.