Consider a point to point link needs a beam which is directed asclose as possible to the other antenna. This will minimizeinterference between different communications systems, as well asmaximizing the power transfer on a given link. For the particular antenna of interest the electric field pattern peaks along thepositive z axis with |E(θ, φ)|2 ∝cos8θ for 0 < θ < 900 andzero for 900 < θ < 1800.
Find the gain of the end fire antenna. You can use the constraintthat the integral of G(θ, φ) over the sphere =4π.