Two identical smooth uniform spheres \(A\) and \(B\), of equal radii and each of mass \(m\), move on a smooth horizontal surface and collide. Immediately before collision, their speeds are \(2u\) and \(3u\) respectively.

Sphere \(A\)'s direction of motion makes an angle \(\theta\) with the line of centres, and sphere \(B\)'s direction of motion is perpendicular to that of \(A\). After the collision, \(B\) moves perpendicular to the line of centres. The coefficient of restitution between the spheres is \(\dfrac13\).

(a) Find \(\tan\theta\).

(b) Find the total loss of kinetic energy as a result of the collision.

(c) Find, in degrees, the angle through which the direction of motion of \(A\) is deflected.