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\\
(1) $\pm \sqrt { 2 }$\\
(2) $\pm 1$\\
(3) $\pm \frac { 1 } { \sqrt { 2 } }$\\
(4) $\pm 2$