Electric field radiated by an antenna, in the far zone, can be approximated by
$0^\circ \le \theta \le 180^\circ$
$\bar{E}_a \approx \bar{E}_a \left| \cos^{1.5}(\theta) \right| \frac{e^{-jkr}}{r} \hat{\theta}$, $0^\circ \le \phi \le 360^\circ$
Find a mathematical expression for the directivity of the antenna.