Two smooth uniform spheres \(A\) and \(B\), of equal radii, have masses \(m\) and \(2m\) respectively. They collide on a smooth horizontal surface.

Before impact, sphere \(A\) has speed \(u\) along the line of centres, and sphere \(B\) has speed \(\dfrac12u\) with its direction making an angle \(\theta\) with the line of centres.

After the collision, the direction of motion of \(A\) is reversed and its speed is reduced to \(\dfrac14u\). The direction of motion of \(B\) again makes an angle \(\theta\) with the line of centres, but on the opposite side of the line of centres. The speed of \(B\) is unchanged.

Find the coefficient of restitution between the spheres.