Comb + Geo = Tension

Let $ABC$ be a triangle with $AB = AC$ . The angle bisectors of $A$ and $B$ meet the sides $BC$ and $AC$ in $D$ and $E$ , respectively. Let $K$ be the incenter of the triangle $ADC$ . Suppose that $\angle BEK= \dfrac{\pi}{4}$ . Find sum of all possible values of $\angle BAC$ .