Fishy Volume

Calculus Level 3

This is the graph of \(r=\frac{\sin4\theta}{\sin\theta}\) in polar coordinates.

Rotating the graph about the \(x\)-axis produces a volume of \(\frac{a}{b}\pi\), where \(a\) and \(b\) are coprime positive integers.

What is \(a+b?\)

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