\(A B\) and \(B C\) are two fixed smooth vertical barriers on a smooth horizontal surface, with angle \(A B C=60^{\circ}\). A particle of mass \(m\) is moving with speed \(u\) on the surface. The particle strikes \(A B\) at an angle \(\theta\) with \(A B\). It then strikes \(B C\) and rebounds at an angle \(\beta\) with \(B C\) (see diagram). The coefficient of restitution between the particle and each barrier is \(e\) and \(\tan \theta=2\).

The kinetic energy of the particle after the first collision is \(40 \%\) of its kinetic energy before the first collision.
(a) Find the value of \(e\).

(b) Find the size of angle \(\beta\).