Ed's trigonometric expression

Algebra Level 3

As \( \theta\) ranges over all real values, the maximum value of \( \frac{ \sin^3 \theta \cos \theta }{ \tan^2 \theta + 1} \) can be written as \( \frac{a}{b} \), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

This problem is posed by Ed M.

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