Ratio of Areas of Trinagles

$E$ and $F$ are two points on sides $BC$ and $CD$ of square $ABCD$ , respectively, and satisfy $\overline{BE}=\overline{CF}$ . Let $P$ be the intersection point of the line segments $AE$ and $BF$ . If the ratio of the areas of triangles $ABP$ and $BEP$ is $9:1$ and $\angle BAE=\theta$ , what is the value of $11\sqrt{10} \cos \theta?$