Hi Shenghui, Very nice post! I have recently published one way to prove the theorem: https://www.parabola.unsw.edu.au/sites/default/files/2024-09/vol60_no2_7.pdf Please let me know your thoughts.
Regards, Ajay
Vlogger Tim Ricchuiti made another nice video showing the proof at https://www.youtube.com/watch?v=p6j2nZKwf20 .