Angle at the centre for which a minor segment is one third of the triangle on the same chord

The diagram shows a circle with centre \(O\) and radius \(r\text{ cm}\). The points \(A\) and \(B\) lie on the circle, and \(\angle AOB=\theta\) radians, where \(0<\theta<\pi\). The region between the chord \(AB\) and the minor arc \(AB\) is shaded.

The area of the shaded region is one third of the area of triangle \(AOB\). Find the value of \(\theta\).[5]