A hollow uniform hemisphere of radius R is pressed against a smooth vertical wall by a force F at point P as shown. The force F makes an angle $\mathrm{\theta }$ with vertical and its line of action is passing through center of   hemisphere. Center of mass of hemisphere is at distance $\frac{\mathrm{R}}{2}$ from the center. What is the minimum value of tan$\mathrm{\theta }$ for equilibrium?