3. Given that the two foci and the center of the ellipse divide the distance between the two directrices into four equal parts, then the angle between the line connecting one focus to the endpoints of the minor axis is

保留源文本的换行和格式，直接输出翻译结果。 

(Note: The last sentence is a repetition of the instruction and should not be part of the translated text. Here is the corrected version without the repetition:)

3. Given that the two foci and the center of the ellipse divide the distance between the two directrices into four equal parts, then the angle between the line connecting one focus to the endpoints of the minor axis is
3. Let the standard equation of the ellipse be $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$. From the problem, we know $\frac{a^{2}}{c}=2 c$, thus $2 c^{2}=a^{2}=b^{2}+c^{2}$, $\therefore b=c$, so the angle is $90^{\circ}$.