# Why does 0 = 1? Cos 0 = 1

Geometry Level 5

$\large \prod_{r=0}^3 \left [ 4\sin(3 \cdot 5^r x) \sin(5^r x) - 1 \right ] = 1$

Suppose $$x$$ satisfies the equation above, find the total number of solutions of $$x$$ that falls in the range $$(0, \pi)$$.

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