3. A light rod \(A B\) of length \(2 a\) has a particle \(P\) of mass \(m\) attached to \(B\). The rod is rotating in a vertical plane about a fixed smooth horizontal axis through \(A\). Given that the greatest tension in the rod is \(\frac { 9 m g } { 8 }\), find, to the nearest degree, the angle between the rod and the downward vertical when the speed of \(P\) is \(\sqrt { \left( \frac { a g } { 20 } \right) }\).