The value of $3\tan^{-1}\left(\dfrac{1}{2}\right) = \ldots$

The value of $\cot^{-1}\left[\dfrac{\sqrt{1 - \sin x} + \sqrt{1 + \sin x}}{\sqrt{1 - \sin x} - \sqrt{1 + \sin x}}\right]$, where $x \in \left(0, \dfrac{\pi}{2}\right)$ is...

If $(\tan^{-1}x)^2 + (\cot^{-1}x)^2 = \dfrac{5\pi^2}{8}$, then the value of $x$ is equal to...

$\cos\left(\cos^{-1}\left(-\dfrac{1}{2}\right) + \dfrac{\pi}{3}\right) =$