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If the curve \( x^{2}+2 y^{2}=2 \) intersects the line \( x+y=1 \) at two points \( P \) and \( Q \), then the angle subtended by the line
\( P \) segment \( P Q \) at the origin is: [JEE Main-2021 (Fabruary)]

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(a) \( \frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{4}\right) \)
(b) \( \frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{4}\right) \)
(c) \( \frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{3}\right) \)
(d) \( \frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{3}\right) \)
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