GoGeometry Action 105!

Creation of this applet was inspired by a tweet from Antonio Gutierrez. You can move the LARGE WHITE VERTICES of the triangle anywhere you'd like AT ANY TIME. You can also move the 2 LARGE BLUE POINTS anywhere you'd like at any time. You can adjust the size of the pink angle by using the pink slider. How can we formally prove the phenomenon dynamically illustrated here?

Quick (Silent) Demo