For a positive integer \( n \), let \( f_{n}(\theta)=\frac{\tan \theta}{2}(1+\sec \theta) \) \( ...

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For a positive integer \( n \), let \( f_{n}(\theta)=\frac{\tan \theta}{2}(1+\sec \theta) \) \( (1+\sec 2 \theta) \ldots\left(1+\sec 2^{n} \theta\right) \), then
(a) \( f_{2}\left(\frac{\pi}{16}\right)=0 \)
(b) \( f_{3}\left(\frac{\pi}{32}\right)=-1 \)
(c) \( f_{4}\left(\frac{\pi}{64}\right)=-1 \)
(d) \( f_{5}\left(\frac{\pi}{128}\right)=1 \)
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