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Consider \( f(x)=\tan ^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), x \in\left(0, \frac{\pi}{2}\right) . \mathrm{A} \) normal to \( y=f(x) \) at \( x=\frac{\pi}{6} \) also passes through the point:
[JEE Main-2016]
(1) \( (0,0) \)
(2) \( \left(0, \frac{2 \pi}{3}\right) \)
(3) \( \left(\frac{\pi}{6}, 0\right) \)
(4) \( \left(\frac{\pi}{4}, 0\right) \)
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