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Let, \( E_{1} \) and \( E_{2} \) be two ellipse having the same centre and such that foci of \( E_{1} \) lie on \( E_{2} \) and foci of \( E_{2} \) lie on \( E_{1} \). Lengths of major axes of \( E_{1} \) and \( E_{2} \) are equal and are inclined at angle of \( \theta \). Let eccentricity of \( E_{1} \) be \( e_{1} \) and eccentricity of \( E_{2} \) be \( e_{2} \).
If \( \theta=\frac{\pi}{4} \), then \( \frac{2}{e_{1}^{2} e_{2}^{2}}\left(e_{1}^{2}+e_{2}^{2}-1\right) \) equals
(a) \( -1 \)
(b) 0
(c) 1
(d) \( \sqrt{2} \)
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