A value of $tan^{-1}\begin{Bmatrix}sin\left(cos^{-1}\sqrt{\frac{2}{3}}\right)\end{Bmatrix}$, is

$\frac{\pi}{4}$ $\frac{\pi}{2}$ $\frac{\pi}{3}$ $\frac{\pi}{6}$

$\frac{\pi}{6}$

$tan^{-1}\begin{Bmatrix}sin\left(cos^{-1}\sqrt{\frac{2}{3}}\right)\end{Bmatrix}$ $=tan^{-1}\begin{Bmatrix}sin\left(sin^{-1}\sqrt{\frac{1}{3}}\right)\end{Bmatrix}=tan^{-1}\frac{1}{\sqrt{3}}=\frac{\pi}{6}$