# Bulgaria National Olympiad Problem 4

Algebra Level 5

For any real number $$b$$, let $$f(b)$$ denote the maximum of the function $$|\sin x+\frac{2}{3+\sin x}+b|$$ over all $$x \in \mathbb{R}$$. Find the minimum of $$f(b)$$ over all $$b \in \mathbb{R}$$.

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