Find the principal value of each of the following:

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

Find the principal value of each of the following:

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

Find the principal value of each of the following:

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

Find the principal value of each of the following:

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

Find the principal value of each of the following: ${\sin }^{-1}\left(\tan \frac{5\pi }{4}\right)$