Two uniform smooth spheres \(A\) and \(B\) of equal radii have masses \(5m\) and \(4m\), respectively. Sphere \(A\) is moving with speed \(u\) on a horizontal surface when it collides with sphere \(B\), which is at rest. Immediately before the collision, \(A\)'s direction of motion makes an angle \(\theta\) with the line of centres. The coefficient of restitution between the spheres is \(e\).

(a) Show that the speed of \(B\) after the collision is \(\dfrac{5u(1+e)\cos\theta}{9}\).

After the collision the kinetic energy of \(A\) is equal to the kinetic energy of \(B\).

(b) Given that \(\tan\theta=\dfrac{2}{3}\), find the value of \(e\).