The tangent at \( 3 \sqrt{3} \cos \theta, \sin \theta) \) is drawn to the ellipse \( \frac{x^{2}...

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The tangent at \( 3 \sqrt{3} \cos \theta, \sin \theta) \) is drawn to the ellipse \( \frac{x^{2}}{27}+y^{2}=1 \). Then the value of \( \theta \) such that the sum of intercepts on axes made by the tangent is minimum is
(a) \( \frac{\pi}{3} \)
(b) \( \frac{\pi}{6} \)
(c) \( \frac{\pi}{8} \)
(d) \( \frac{\pi}{4} \)
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