Let \(a\), \(b\) and \(c\) be positive real numbers that satisfy the following equations:
\[a^2+b^2+\sqrt{3}ab=727\] \[a^2+c^2+\sqrt{3}ac=829\] \[b^2+c^2-bc=39\]
If \(a+b+c=d+f \sqrt{3}\), find \(df\).

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