In triangle $ABC$, $\angle C = 48^\circ$. $D$ is any point on $BC$, such that $\angle CAD = 18^\circ$ and $AC = BD$. Find $\angle ABD.$
I tried to make some constructions: draw a line through $D$ parallel to $AC$; draw a line through $C$ which makes $66$ degrees with $AC$. None of them have been useful. It feels like I am trying to force the formation of congruent triangles, and that doesn't work. Please help.