${\sin }^{-1}\left(\sin \frac{2\pi }{3}\right)+{\cos }^{-1}\left(\cos \frac{7\pi }{6}\right)+{\tan }^{-1}\left(\tan \frac{3\pi }{4}\right)$  is equal to 

$$\begin{gathered} {\sin }^{-1}\left(\sin \frac{2\pi }{3}\right)+{\cos }^{-1}\left(\cos \frac{7\pi }{6}\right)+{\tan }^{-1}\left(\tan \frac{3\pi }{4}\right) \\ ={\sin }^{-1}\left(\sin (\pi -\frac{2\pi }{3})\right)+{\cos }^{-1}\left(\cos (2\pi -\frac{7\pi }{6})\right)-{\tan }^{-1}\left(\tan (\pi -\frac{3\pi }{4})\right) \\ =\frac{\pi }{3}+\frac{5\pi }{6}-\frac{\pi }{4}=\frac{11\pi }{12} \end{gathered}$$