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Let \( \frac{-\pi}{6}\theta\frac{-\pi}{12} \). Suppose \( \alpha_{1} \) and \( \beta_{1} \) are the roots
\( \mathrm{P} \)
W of the equation \( x^{2}-2 x \sec \theta+1=0 \) and \( \alpha_{2} \) and \( \beta_{2} \) are the roots of the equation \( x^{2}+2 x \tan \theta-1=0 \). If \( \alpha_{1}\beta_{1} \) and \( \alpha_{2}\beta_{2} \), then \( \alpha_{1}+\beta_{2} \) equals
(1) \( 2(\sec \theta-\tan \theta) \)
(2) \( 2 \sec \theta \)
(3) \( -2 \tan \theta \)
(4) 0
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