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