MathNet 2019-part-02 — 184 problems (EN–VI) Question 111

Let $\triangle ABC$ be a triangle such that $\angle ABC = 2\angle BCA$, and the angle bisector of $\angle BAC$ intersects the side $\overline{BC}$ at point $D$ so that $|AB| = |CD|$. Find $\angle CAB$. (Estonia 2002)