MathNet 2018-part-02 — 181 problems (EN–VI) Question 20

Let $\triangle ABC$ be a triangle such that $\angle CAB = 2\angle ABC$. A point $D$ is given in the interior of the triangle $\triangle ABC$, such that $|AD| = |BD|$ and $|CD| = |AC|$. Prove that $\angle ACB = 3\angle DCB$.