Two smooth vertical walls meet at right angles. The smooth sphere \(A\), with mass \(m\), is at rest on a smooth horizontal surface and is at a distance \(d\) from each wall. An identical smooth sphere \(B\) is moving on the horizontal surface with speed \(u\) at an angle \(\theta\) with the line of centres when the spheres collide.

After the collision, the spheres take the same time to reach a wall. The coefficient of restitution between the spheres is \(\dfrac12\).

(a) Find the value of \(\tan\theta\).

(b) Find the percentage loss in the total kinetic energy of the spheres as a result of this collision.