An antenna far field radiation pattern is independent of \(\phi\) and the varies versus \(\theta\) as follows:

\[
F(\theta, \phi)=\left\{\begin{array}{rr}
1 & \frac{\pi}{2}-\alpha \leq \theta \leq \frac{\pi}{2}+\alpha \\
0 & \text { elsewhere }
\end{array}ight\}
\]

Compute the directivity.