AHA effect

In quadrilateral ABCD, angles at A and B are given.
Find all angles at C and D.

Obvious to get ADB and ACD, but the two others ???
Yes, you could use the sinus law to get a complicated trigonometric equation...

The aim of this problem here is to get a "AHA" effect, which results into an elementar method.
Without any trigonometry at all. Hint



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