What if answer comes an irrational number

Level 2

The value of sinπ14×sin3π14×sin5π14×sin7π14×sin9π14×sin11π14×sin13π14sin\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.a1a2a3a4......an0.a_1a_2a_3a_4......a_n where 0a1,a2,a3,.....,an90 \leq a_1,a_2,a_3,.....,a_n \leq 9 & a1,a2,a3,.....,anIntegersa_1,a_2,a_3,.....,a_n \in Integers.

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


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