(1) Without loss of generality take coordinate axes so that A is the point(0,0,1), the xz-plane contains the point C and the yz-plane contains the point B.

(2) Thinking of A as the North Pole then C has latitude u and longitude 0 and B has latitude v and longitude p/2.

(3) Find the 3D coordinates of B and C. Where the origin O is the centre of the sphere OA, OB and OC are vectors of unit length.

(4) Use scalar products and vectors OA, OB and OC to find the lengths of the arcs AB, BC and CA in terms of u and v. The required result follows.