Interesting Incircle

Geometry 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 \(PQRS\).

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