3 A fixed hollow sphere with centre \(O\) has a smooth inner surface of radius \(a\). A particle \(P\) of mass \(m\) is projected horizontally with speed \(2 \sqrt { } ( a g )\) from the lowest point of the inner surface of the sphere. The particle loses contact with the inner surface of the sphere when \(O P\) makes an angle \(\theta\) with the upward vertical.
- Show that \(\cos \theta = \frac { 2 } { 3 }\).
- Find the greatest height that \(P\) reaches above the level of \(O\).