2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a1365c54-4910-449b-b270-c56c1bc5a751-04_479_853_246_607}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
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 point \(A\) which lies above a smooth horizontal table. The particle \(P\) moves in a horizontal circle on the table with the string taut. The centre of the circle is the point \(O\) on the table, where \(A O\) is vertical and the string makes a constant angle \(\theta ^ { \circ }\) with \(A O\), as shown in Figure 2.
Given that \(P\) moves with constant angular speed \(\sqrt { \frac { 2 g } { a } }\), find the range of possible values of \(\theta\)