Angle at the centre for which a minor segment is a given fraction of the rest of the circle

In the diagram, the circle has 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 minor segment cut off by the chord \(AB\) is shaded.

The area of the shaded segment is one quarter of the area of the unshaded part of the circle. Find the value of \(\theta\).[5]