The value of ${\sin }^{-1}\left\{\cot \left[{\sin }^{-1}\sqrt{\frac{2-\sqrt{3}}{4}}+{\cos }^{-1}\left(\frac{\sqrt{12}}{4}\right)+{\sec }^{-1}\sqrt{2}\right]\right\}$ is

Given expression
$\begin{array}{l}={\sin }^{-1}\cot \left\{{\sin }^{-1}\left.\sqrt{\frac{2-\sqrt{3}}{4}}+{\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)+{\cos }^{-1}\left(\frac{1}{\sqrt{2}}\right)\right]\right.\\ ={\sin }^{-1}\cot \left\{{\sin }^{-1}\sqrt{\frac{2-\sqrt{3}}{4}}+{\cos }^{-1}\sqrt{\frac{2-\sqrt{3}}{4}}\right\}\\ ={\sin }^{-1}\left\{\cot \frac{\mathrm{\pi }}{2}\right\}={\sin }^{-1}0=0\end{array}$