Level
2

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 $\displaystyle \sum_{i=1}^n a_i$