It's definitely correct, and quite trivial to verify. It's possible it has been discovered before, but none of the proof compilations I've seen (e.g. cut-the-knot) has it, and the trigonometric proofs I can find involve using angle-sums (https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf).

This is definitely a much more elegant proof than the angle-sum proofs.