Telltale signs

Consider an acute triangle $ABC$ with $X$ as the foot of the perpendicular from $A$ to $BC$ . Let the circle $\Omega$ with $AX$ as the diameter intersect $AB$ and $AC$ at $D$ and $E$ respectively. Let $BE$ and $CD$ intersect circle $\Omega$ at $E'$ and $D'$ respectively. If the measures of the angles $E'AX, EE'D', D'AX$ and $EBC$ are $a,b,c$ and $d$ respectively, and $\dfrac{\sin (a) \sin(b)}{\sin(c) \sin(d)} = \dfrac xy$ for coprime positive integers $x$ and $y$ , calculate $x+y$ .