# The smiling Buddha

Level pending

For each $$b \in \mathbb{R}$$, define

$f(b) =\max_{x \in \mathbb{R} } ( |b+sin(x)+\frac{2}{3+sin(x)}|)$

The minimum value of $$f(b)$$, is of the form $$\frac{s}{t},$$ where $$s$$ and $$t$$ are coprime integers . Find $$s + t$$.

Here $$| \cdot |$$ denote modulus function and $$\max( \cdot )$$ denotes the maximum function.