No Calculus please

$\large \lim _ { n\rightarrow \infty }{ { \left( \prod _{ r=1 }^{ n }{ \sin { \left( \frac { r\pi }{ 4n } \right) \cos { \left( \frac { r\pi }{ 4n } \right) } } } \right) }^{ \frac { 1 }{ n } } } = \frac { a }{ b }$

If the equation holds true for positive integers $a$ and $b$ , find the smallest value of $a + b$ .