KöMaL 2021 B5183

Side $AB$ of a triangle $ABC$ has unit length, $\angle BAC = 60^{\circ}$, $\angle ACB =100^{\circ}$ and the midpoint of side $BC$ is $F$. $D$ is a point on side $AB$ such that $DB = FB$. Find the exact value of $T_{ABC\triangle}+2T_{FBD\triangle}$, where $T_{ABC\triangle}$ denotes the area of triangle $ABC$. ($T$ means the area of the triangle of the triangle named in the index.)