Let $ABC$ be a triangle with $AB=AC$. The$\angle CAB$  and $\angle ABC$ meet the sides $BC$ and $CA$ at $D$ and $E$, respectively. Let $K$ be the incentre of triangle $ADC$. Suppose that $\angle BEK=45^\circ$. Find the sum of all possible values of $\angle CAB$.

Source: IMO