$$ \text { Let } f(x)=\cos ^{-1}(3 x-1) \text {, then domain of } f(x) \text { is equal to } $$

$$ \text { The value of } \sin ^{-1}\left[\cos \left(39 \frac{\pi}{5}\right)\right] \text { is } $$

The value of $$\sin \left[ {2{{\cos }^{ - 1}}{{\sqrt 5 } \over 3}} \right]$$ is

The solution of $${\tan ^{ - 1}}x + 2{\cot ^{ - 1}}x = {{2\pi } \over 3}$$ is