What if answer comes an irrational number

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The value of \[sin\frac{\pi}{14} \times sin\frac{3\pi}{14} \times sin\frac{5\pi}{14} \times sin\frac{7\pi}{14} \times sin\frac{9\pi}{14} \times sin\frac{11\pi}{14} \times sin\frac{13\pi}{14}\] is \(0.a_1a_2a_3a_4......a_n\) where \(0 \leq a_1,a_2,a_3,.....,a_n \leq 9\) & \(a_1,a_2,a_3,.....,a_n \in Integers\).

Find \(\displaystyle \sum_{i=1}^n a_i\)


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