True or False: The principal value of $\sin^{-1}\begin{bmatrix}\cos\bigg(\sin^{-1}\frac{1}{2}\bigg)\end{bmatrix}\;is\;\Large {\frac{\pi}{3}}$

Question

$\begin{array}{1 1} \large {\frac{\pi}{3}} \\ \large {\frac{\pi}{6}} \\ \large {\frac{2\pi}{3}} \\ \large {\frac{\pi}{4}} \end{array} $