Ed's trigonometric expression

Algebra Level 3

As θ \theta ranges over all real values, the maximum value of sin3θcosθtan2θ+1 \frac{ \sin^3 \theta \cos \theta }{ \tan^2 \theta + 1} can be written as ab \frac{a}{b} , where aa and bb are coprime positive integers. What is the value of a+ba+b?

This problem is posed by Ed M.

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