# 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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