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\(O A B C\) is the cross-section through the centre of mass of a uniform prism of weight 20 N . The crosssection is in the shape of a sector of a circle with centre \(O\), radius \(O A = r \mathrm {~m}\) and angle \(A O C = \frac { 2 } { 3 } \pi\) radians. The prism lies on a plane inclined at an angle \(\theta\) radians to the horizontal, where \(\theta < \frac { 1 } { 3 } \pi\). OC lies along a line of greatest slope with \(O\) higher than \(C\). The prism is freely hinged to the plane at \(O\). A force of magnitude 15 N acts at \(A\), in a direction towards to the plane and at right angles to it (see diagram). Given that the prism remains in equilibrium, find the set of possible values of \(\theta\).