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