# 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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