Show that the angles ACB and DCF are equal

anonym4=

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Given a parallelogramm ABCD with the diagonal intersection point M, such that the circumcircle of the triangle ABM intersects the line AD in a point E (different from A) and the circumcircle of the triangle EMD intersects the line BE in a point F (different from E).
Show that the angles ACB and DCF are equal.

I have provided a visualisation of the problem, but I don't even know where to start. I'd love to hear all your ideas on this one
 

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