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Let \( M=\left[\begin{array}{cc}\sin ^{4} \theta & -1-\sin ^{2} \theta \\ 1+\cos ^{2} \theta & \cos ^{4} \theta\end{array}\right]=\alpha I+\beta M^{-1} \)
P where \( \alpha=\alpha(\theta) \) and \( \beta=\beta(\theta) \) are real number, and \( \mathrm{I} \) is the

W \( 2 \times 2 \) identity matrix. If
\( \alpha^{*} \) is the minimum of the set \( \{\alpha(\theta): \theta \in[0,2 \pi)\} \) and \( \beta^{*} \) is the minimum of the set \( \{\beta(\theta): \theta \in[0,2 \pi)\} \), then the value of \( \alpha^{*}+\beta^{*} \) is
[JEE Advanced-2019]
\( (1)-\frac{37}{16} \)
\( (2)-\frac{29}{16} \)
(3) \( -\frac{31}{16} \)
(4) \( -\frac{17}{16} \)
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