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

0

$ sin^{-1}\begin{Bmatrix}cot\left(sin^{-1}\sqrt{\frac{2-\sqrt{3}}{4}}+cos^{-1}\frac{\sqrt{12}}{4}+sec^{-1}\sqrt{2}\right)\end{Bmatrix}$

$ sin^{-1}\begin{Bmatrix}cot\left(sin^{-1}\frac{\sqrt{3}-1}{2\sqrt{2}}+cos^{-1}\frac{\sqrt{3}}{2}+sec^{-1}\sqrt{2}\right)\end{Bmatrix}$

$ sin^{-1}\begin{Bmatrix}cot \left(\frac{\pi}{12}+\frac{\pi}{6}+\frac{\pi}{4}\right)\end{Bmatrix}= sin^{-1}\left(cot\frac{\pi}{2}\right)= sin^{-1} 0=0$