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 \(\frac{\Phi}{\sqrt{n}}\), where the value of \(n\) is \_\_\_\_.
\includegraphics[width=0.3\linewidth]{ph8.png}