JEE Main 2012 — Trigonometry

The value of $\cos 255^{\circ}+\sin 195^{\circ}$ is

Suppose $\theta$ and $\phi(\neq 0)$ are such that $\sec (\theta+\phi)$, sec $\theta$ and $\sec (\theta-\phi)$ are in A.P. If $\cos \theta=k \cos \left(\frac{\phi}{2}\right)$ for some $k$, then $k$ is equal to

A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right)$ is