Conic Sections and Parametric Equations · Superchallenge problem

Let $F_1$ and $F_2$ be the left and right foci of the hyperbola $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$. The circle with diameter $F_1F_2$ meets the asymptote $y=\dfrac bax$ at a point $M$ in the first quadrant, and $\angle MF_1F_2=30^\circ$. Find the eccentricity of the hyperbola.