No Calculus please

Calculus Level 3

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

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

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