Let \( f:(-1,1) \rightarrow R \) be such that \( f(\cos 4 \theta)=\frac{2}{2-\sec ^{2} \theta} \...
Let \( f:(-1,1) \rightarrow R \) be such that \( f(\cos 4 \theta)=\frac{2}{2-\sec ^{2} \theta} \). \( \theta \in\left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{4}, \frac{\pi}{2}\right) \). Then the values of \( f\left(\frac{1}{3}\right) \) is /are
(a) \( 1-\sqrt{\frac{3}{2}} \)
(b) \( 1+\sqrt{\frac{3}{2}} \)
(c) \( 1-\sqrt{\frac{2}{3}} \)
(d) \( 1+\sqrt{\frac{2}{3}} \)
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