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For some \( \theta \in\left(0, \frac{\pi}{2}\right) \), if the eccentricity of the
P
W hyperbola, \( x^{2}-y^{2} \sec ^{2} \theta=10 \) is \( \sqrt{5} \) times the eccentricity of the ellipse, \( x^{2} \sec ^{2} \theta+y^{2}=5 \), then the length of the latus rectum of the ellipse, is:
(1) \( \sqrt{30} \)
(2) \( 2 \sqrt{6} \)
(3) \( \frac{4 \sqrt{5}}{3} \)
(4) \( \frac{2 \sqrt{5}}{3} \)
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