An antenna has a conical radiation pattern with a normalized radiation intensity U$(0)=1$ for $0$ between$0\backslash$deg and $45\backslash$deg and zero intensity for $0$ between $450$ and $180\backslash$deg $.$ The pattern is independent of the azimuth angle g$.$ Find $($a$)$ the pattern solid angle and $($b$)$ the directivity.