Find the principal value of each of the following:

${\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

Find the principal value of each of the following: ${\cos }^{-1}\left(-\frac{1}{\sqrt{2}}\right)$

Find the principal value of each of the following:

${\cos }^{-1}\left(\sin \frac{4\pi }{3}\right)$

Find the principal value of each of the following: ${\cos }^{-1}\left(\tan \frac{3\pi }{4}\right)$

Find principal value: ${\cos }^{-1}\left(\frac{1}{2}\right)-2{\sin }^{-1}\left(-\frac{1}{2}\right)$

For the principal values, evaluate each of the following: ${\sin }^{-1}\left(-\frac{1}{2}\right)+2{\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

For the principal values, evaluate each of the following: ${\sin }^{-1}\left(-\frac{\sqrt{3}}{2}\right)+{\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Find the principal value of each of the following: ${\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$