Three uniform small spheres \(A, B\) and \(C\) have equal radii and masses \(2 m, 4 m\) and \(m\) respectively. The spheres are moving in a straight line on a smooth horizontal surface, with \(B\) between \(A\) and \(C\). The coefficient of restitution between each pair of spheres is \(e\). Spheres \(A\) and \(B\) are moving towards each other with speeds \(2 u\) and \(u\) respectively. The first collision is between \(A\) and \(B\).
(i) Find the velocities of \(A\) and \(B\) after this collision.

Sphere \(C\) is moving towards \(B\) with speed \(\frac{4}{3} u\) and now collides with it. As a result of this collision, \(B\) is brought to rest.
(ii) Find the value of \(e\).

(iii) Find the total kinetic energy lost by the three spheres as a result of the two collisions.