Never knew about that equation! That's cool. Angles are always such a pain. In my experience it's worth applying trigonometric identities and working in terms

Never knew about that equation! That's cool. Angles are always such a pain. In my experience it's worth applying trigonometric identities and working in terms of unit vectors, sines, and cosines instead of using angles directly. In this case angles seem unavoidable, though: acos(tan(x)*tan(y)) doesn't simplify to anything useful.