Sum of Series with Trigonometric Terms: Seeking Method to Find Exact Value

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Hi, I need to find the sum of such series:
\sum_{n=1}^{\infty}\sin{\frac{\pi}{2^n}}
i know that it's sum is less than \pi but i don't know how to find the exact value.
thanks in advance for any help or clues
 
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What have you tried doing?
 
first of all i'd like to correct myself as i don't really need to find that sum. i was just wondering whether my mathematical knowledge is big[?] enough to solve this problem, so what should I have really asked about is: what method would you choose to find that sum.
What have you tried doing?
I have used the comparative criterion (precisely this inequality: sin {x}\leq x)to find out that this series is convergent and that it's sum is equal or less than \pi, but i don't know what to do next. could you tell me what is the level of difficulty of this problem? is the solution rather complicated or can it be presented in a few lines? or which mathematical terms should i know in order to solve it on my own?
 
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