Rod and Circle

A smooth uniform rod of mass 𝑚 and length 2𝑎 is freely hinged to the ground at the point A between two smooth parallel vertical walls. The rod's other end, B, rests against one of the walls, and a uniform circular lamina of mass $\frac{m}{2}$ is in contact with the other wall at a point P and with the rod at a point Q. The rod and the lamina rest in equilibrium in the same vertical plane which is perpendicular to both walls.

Given that the rod is inclined at an angle 𝜃=60∘ to the horizontal and that the distance 𝐴𝑄= $\frac{2}{3}$ 𝑎, find the magnitude of the reaction force at B.