What is the principal value of $\sec^{-1}\left(\frac{2 \sqrt{3}}{3}\right)$?

Explanation

1. 01

   Find the angle $\theta$ in the branch $[0, \pi] - \left\{\frac{\pi}{2}\right\}$ with $\sec \theta = \frac{2 \sqrt{3}}{3}$.

2. 02

   That angle is $\frac{\pi}{6}$.