Two uniform smooth spheres \(A\) and \(B\), with equal radii and masses \(2m\) and \(m\), collide directly. Initially \(A\) moves with speed \(u\), and \(B\) is stationary. After the collision, both move in the same direction with speeds \(v_A\) and \(v_B\). The kinetic energy of \(B\) is \(\frac92\) times the kinetic energy of \(A\).

(a) Show that \(v_B=\frac65u\).

Sphere \(B\) then collides with a fixed vertical barrier. Immediately before the collision, its direction makes angle \(\alpha\) with the barrier; immediately after, its direction makes angle \(\beta\) with the barrier. The coefficient of restitution is \(\frac45\), and its speed is reduced to \(\frac{12\sqrt5}{25}u\).

(b) Find \(\sin(\alpha+\beta)\).