sequences and series - Find the result of $sum_{n=1}^{infty} sinleft(frac{1}{2^n}right)$

Applying ratio test, we can prove this series $\displaystyle \sum_{n=1}^{\infty} \sin\left(\frac{1}{2^n}\right)$ converges.

How can we calculate or estimate the sum?

Any help is appreciated, thank you.