In equilateral triangle \(ABC\), points \(D\) and \(E\) trisect \(BC\). If \(\sin(DAE)\) can be expressed as \(\frac{a\sqrt{b}}{c}\) where \(a\) and \(b\) are in the simplest form and \(b\) is a non perfect square, find \(a+b+c\).

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