Two uniform rods \(A B\) and \(A C\) have lengths \(2 a\) and \(4 a\) and weights \(W\) and \(2 W\) respectively. They are freely hinged together at \(A\) and rest in equilibrium in a vertical plane with \(B\) and \(C\) in contact with two rough parallel vertical walls. The plane containing the rods is perpendicular to the walls. The rods \(A B\) and \(A C\) each make an angle \(\beta\) with the vertical (see diagram). Show that the magnitude of the frictional force acting on \(A B\) at \(B\) is \(\frac { 5 } { 4 } W\). Given that the coefficient of friction at \(B\) and at \(C\) is \(\mu\), find the set of possible values of \(\mu\) in terms of \(\beta\).