Functions

Let the range of the function \(f(x)=\frac{1}{2+\sin 3 x+\cos 3 x}, x \in \mathbb{R}\) be \([a, b]\). If \(\alpha\) and \(\beta\) ar respectively the A.M. and the G.M. of \(a\) and \(b\), then \(\frac{\alpha}{\beta}\) is equal to