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

Question

$\begin{array}{1 1}(1) (0,0) \\(2) (0, \large\frac{2 \pi}{3}) \\ (3) (\large\frac{\pi}{6},0)\\ (4) (0, \large\frac{\pi}{4},0)\end{array} $