3. If the distance between the two directrices of an ellipse is equal to twice the distance between the two foci, then its eccentricity $e=$

保留了源文本的换行和格式。
$$
\frac{a^{2}}{c}=2 c \Rightarrow e^{2}=\frac{c^{2}}{a^{2}}=\frac{1}{2} \Rightarrow e=\frac{\sqrt{2}}{2} .
$$