Angle degree

Let $ABCD$ be a convex quadrilateral whose sides $AD$ and $BC$ are not parallel. Suppose that the circles with diameters $AB$ and $CD$ intersect at two points $E$ and $F$ lying inside the quadrilateral. Let $H_1, H_2, H_3$ be the feet of the perpendiculars from $E$ to the lines $AB$, $BC$, $CD$, respectively. Given that $\angle ABE = 30^\circ$ and $\angle ECD = 40^\circ$, find $\angle H_1H_2H_3$, in degrees.