In a convex quadrilateral ABCD, the angles BCA and BDA are equal. Prove that angles ABD and ACD are also equal

∠BCA and ∠BDA rely on the cut AB and are equal to each other.
So we can draw a circle through points AB and the vertices of these angles. These angles will be inscribed in a circle, based on one arc.
It turns out that we described a circle around a quadrangle.
Note that the angles ABD and ACD are also inscribed and based on the same arc, i.e., using the inscribed angle theorem, we find that they are equal to each other.