Given is the quadrilateral ABCD, and that |AC| = 2|BC|. Further,

\angle ABD = \angle DBC = \angle DAC

Also \angle ADC = 90^{\circ}

Determine the quadrilateral's remaining angles.

I'm not sure how to solve this, but I think it has to do with similarity. I'd prefer a nudge in the right direction rather than a full solution because I'd like to solve it myself, but any help is appreciated.