I think it would be interesting to bundle this as a lesson for high school students. Not necessarily because of the trigonometry, but because it seems very engaging.
It could be a good lead-in to a lesson on straight-edge & compass constructions, which is pretty fun.
Isn't this essentially just projecting a 3d sphere onto a 2d surface, but evaluating the transformation components without putting them in matrix form?
I've just learned about transformation matrix and I'm not sure but I guess so. I would say its essentially about how a human can draw spheres on a paper.