Circumcircle

In acute $\triangle ABC$ , $\angle BAC= \tan^{-1} \left ( \dfrac{3 \sqrt{5}}{7} \right )$ and $AC= \dfrac{2}{3}AB$ . A point $D$ is chosen on $AC$ extended such that $AD= AB$ . The circumcircle of $\triangle CDB$ intersects $AB$ at two points: $E$ and $B$ . If $\dfrac{AE}{AB}= \dfrac{a}{b}$ for some coprime positive integers $a, b$ , find $a+b+3$ .