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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