Lamis theorem proof

Lamis Theorem 

If three forces acting on a particle keep it in equilibrium, each is proportional to the sine of the angle between the other two.

Thus if the forces are P, Q and R and α, β, γ be the angles between Q, R; R, P; and P, Q respectively then if the forces are in equilibrium, we have

Example:    Forces P, Q and R acting along OA, OB and OC, where O is the circumcentre of the triangle ABC are in equilibrium. Show that 

    .

⇒ .