Tangent is drawn to the ellipse $\large\frac{x^2}{27} $$+y^2=1$ at $(3 \sqrt 3 \cos \theta, \sin \theta)$ (where $\theta \in (0, \large\frac{\pi}{2} )$) Then the value of $\theta$ such that sum of intercepts on axis made by this tangent is minimum is

Question

$\begin{array}{1 1}(A)\;\frac{\pi}{3} \\(B)\;\frac{\pi}{6} \\(C)\;\frac{\pi}{8} \\(D)\;\frac{\pi}{4} \end{array}$