Prove that $\displaystyle a_n$ has a limit:

$\displaystyle a_n=\sum_{i=1}^{2^n} sin\frac{i}{2^{2n}}cos\frac{i}{2^{2n}}cos\frac{i}{ 2^{2n-1}}...cos\frac{i}{2^{n+1}}$

The subject is integrals, Riemann's definition and all that... I have no idea how to look for a solution

Thanks!