2013 TJC P2 Q1

The diagram below shows the points \(P\) and \(Q\) on the circumference of a circle with centre \(O\), and radius \(2a\) cm, where \(\angle POQ=\theta \). Points \(P\) and \(Q\) are moving on the circumference so that \(\theta \) is increasing at a constant rate.

Find the acute angle \(\theta \) at the instant when the rate of change of the area of the shaded segment is \(\frac{a}{2}\) times the rate of change of the length of the minor arc \(PQ\).[5]