Fourth circle theorem: 'Angles in a Cyclic Quadrilateral'

Angles in a Cyclic Quadrilateral

Fourth circle theorem:

What's the connection between pairs of opposite angles (α and γ or β and δ)? *

You can use the cursor to move any of points C, D, E or F around the circumference, and hence alter some of the angles.
You can also move point A or B to change the size of the circle.

* Hint: Add the pair of angles!
If you need them, the theorems are summarised here

Tim Devereux, Created with GeoGebra