Two identical smooth spheres \(A\) and \(B\), each of mass \(m\), move on a horizontal surface with speeds \(2u\) and \(u\) respectively when they collide. Immediately before collision, their directions of motion are parallel and opposite, and each makes angle \(\theta\) with the line of centres. After collision, \(B\) moves perpendicular to its initial direction. The coefficient of restitution is \(e\).

(a) Find \(\tan\theta\) in terms of \(e\).

(b) Given that after the collision \(A\) moves perpendicular to the line of centres, find \(\theta\).