Let the side length of the tetrahedron be a. Find CM in terms of a.
∠CAM=60∘sin60∘=CACM⟹CM=2a3
Similarly,DM=2a3
By Toolkit 58 — Law of Cosines, use the Law of Cosines in △CMD.cos(∠CMD)=2(CM)(MD)CM2+MD2−CD2=2(2a3)(2a3)(2a3)2+(2a3)2−a2=23a243a2+43a2−a2=23a22a2=31