# The Trigonometric Pie

Geometry Level pending

$\large f ( \theta) =\frac { \sin ^{ 2 }{ (4\theta } )-\sin ^{ 2 }{ (\theta ) } }{ \sin { (\theta )\sin { (5\theta ) } } }$

Let function $$f(\theta)$$ be defined as above. Find $$\displaystyle \prod _{n=0}^8 \left(f (2^{n-1} \theta)-1\right)$$, where $$\theta =\dfrac \pi {513}$$.

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