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Tangents are drawn from the point \( (\alpha, \beta) \) to the hyperbola \( 3 x^{2}-2 y^{2}=6 \) and are inclined at angles \( \theta \) and \( \phi \) to the \( x \)-axis. If \( \tan \theta \cdot \tan \phi=2 \), prove that \( \beta^{2}=2 \alpha^{2}-7 \).
\( \mathrm{P} \)
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