3. $A B C D E F$ - a regular hexagon with a mirrored inner surface. A light ray exits from point $A$ and after two reflections from the sides of the hexagon (at points $M$ and $N$), it reaches point $D$ (Fig. 1). Find the tangent of angle $E A M$.

![](https://cdn.mathpix.com/cropped/2024_05_06_a51944d10325636e7e98g-1.jpg?height=380&width=368&top_left_y=2374&top_left_x=1575)
Answer: $\frac{1}{3 \sqrt{3}}$.