Question 7
(GBR) Let $ABC$ be a triangle such that $\angle ACB=2\angle ABC$. Let $D$ be the point on the side $BC$ such that $CD=2BD$. The segment $AD$ is extended to $E$ so that $AD=DE$. Prove that
$$\angle ECB+180^\circ=2\angle EBC.$$
$$\angle ECB+180^\circ=2\angle EBC.$$