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Let \( f_{n}(a)=\frac{\sin \alpha+\sin 3 \alpha+\sin 5 \alpha+\ldots+\sin (2 n-1) \alpha}{\cos \alpha+\cos 3 \alpha+\cos 5 \alpha+\ldots+\cos (2 n-1) \alpha} \). Then, the value of \( f_{4}\left(\frac{\pi}{32}\right) \) is equal to
(a) \( \sqrt{2}+1 \)
(b) \( \sqrt{2}-1 \)
(c) \( 2+\sqrt{3} \)
(d) \( 2-\sqrt{3} \)
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