300 Followers problem

Geometry Level 4

\[\prod_{r=1}^{5}\cos\left(\frac{(2r-1)\pi}{20}\right)+\prod_{r=0}^{3}\cos\left(\frac{2^{r}\pi}{15}\right)=\]

This sum has the form \(\dfrac{1}{32}(A + \sqrt{B})\) where \(A\) and \(B\) are integers. What is the value of \(A\times B?\)

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