JEE Advanced 2024 Physics question on Electrostatics

A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle $\theta$ at P, as shown in the figure. When $\theta = 30^\circ$, then the electric flux through the curved surface of the cylinder is $\Phi$. If $\theta = 60^\circ$, then the electric flux through the curved surface becomes $\Phi/\sqrt{n}$, where the value of n is______.