A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(a\). The other end of the string is attached to a fixed point \(O\). The particle completes vertical circles with centre \(O\). The points \(A\) and \(B\) are on the path of \(P\), both on the same side of the vertical through \(O . O A\) makes an angle \(\theta\) with the downward vertical through \(O\) and \(O B\) makes an angle \(\theta\) with the upward vertical through \(O\).

The speed of \(P\) when it is at \(A\) is \(u\) and the speed of \(P\) when it is at \(B\) is \(\sqrt{a g}\). The tensions in the string at \(A\) and \(B\) are \(T_{A}\) and \(T_{B}\) respectively. It is given that \(T_{A}=7 T_{B}\).

Find the value of \(\theta\) and find an expression for \(u\) in terms of \(a\) and \(g\).