Interesting IncircleGeometry Level 4
\(ABC\) is a triangle with \( \angle BAC = 60^\circ \). It has an incircle \(\Gamma\), which is tangential to \(BC\) at \(D\). It is given that \(BD = 3 \) and \(DC = 4 \). What is the value of \( [ABC]^2\)?
Details and assumptions
\([PQRS] \) denotes the area of figure \(PQRS\).