If u, v, w are three non-coplaner unit vectors and α, β, γ are the angle between u and v, v and w, and w and u respectively, and x, y, z are unit vectors along the bisectors of the angle α, β, γ respectively. Prove that [x × y, y × z, z × x] = (1/16) [u v w]2 sec2(α/2)sec2(β/2)sec2(γ/2)