A particle, P$,$ of mass $3$ kg is attached to one end of a light inextensible string. The string passes through a smooth fixed ring, O$,$ and a second particle, Q$,$ of mass $5$ kg is attached to the other end of the string. The particle Q hangs at rest vertically below the ring and the particle P moves with speed $4$ m$/$s in a horizontal circle, as shown in the diagram. The angle between OP and the vertical is $\backslash$theta $.$

a$)$ Find $\backslash$theta