Thank you, that's truly excellent! And although it is a little bit technical and more complex than the more standard proofs, it is exactly what it claims to be,

Thank you, that's truly excellent! And although it is a little bit technical and more complex than the more standard proofs, it is exactly what it claims to be, a non-circular trigonometric proof of the Pythagorean Theorem. They use a key trigonometric identity sin(2*a) = 2*sin(a)*cos(a), which indeed is quite easy to prove without assuming the Pythagorean Theorem.