KöMaL 2022 C1722

In a quadrilateral $ABCD$, sides $AD$ and $DC$ are equal in length. If $\alpha$ denotes the angle $DAB$ then $\angle ABC=2\alpha$, $\angle BCD=3\alpha$ and $\angle CDA=4\alpha$. Prove that side $AB$ is twice as long as side $AD$.