The principal value of $\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$ is

$\tan ^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+\sec ^{-1}\left(\sqrt{\frac{8+4 \sqrt{3}}{6+3 \sqrt{3}}}\right)$ is equal to $.........$

The principal value of ${\sin ^{ - 1}}\left[ {\sin \left( {\frac{{2\pi }}{3}} \right)} \right]$ is

The value of $\sec ^{-1}\left(\frac{1}{4} \sum_{k=0}^{10} \sec \left(\frac{7 \pi}{12}+\frac{k \pi}{2}\right) \sec \left(\frac{7 \pi}{12}+\frac{(k+1) \pi}{2}\right)\right)$ in the interval $\left[-\frac{\pi}{4}, \frac{3 \pi}{4}\right]$ equals

$\cos (\tan ^{ - 1}x) = $

If $\theta \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$,then $\cos^{-1}(\sin \theta)$ is equal to