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 \((0, \pi) \).