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In equilateral \(\triangle ABC\) let points \(D\) and \(E\) trisect \(\overline{BC}\). Then \(\sin \left( \angle DAE \right)\) can be expressed in the form \(\tfrac{a\sqrt{b}}{c}\), where \(a\) and \(c\) are relatively prime positive integers, and \(b\) is an integer that is not divisible by the square of any prime. Find \(a+b+c\).