JEE Math Practice Question

Let a tangent be drawn to the ellipse $${{{x^2}} \over {27}} + {y^2} = 1$$ at $$(3\sqrt 3 \cos \theta ,\sin \theta )$$ where $$0 \in \left( {0,{\pi \over 2}} \right)$$. Then the value of $$\theta$$ such that the sum of intercepts on axes made by this tangent is minimum is equal to :

1. A.$${{\pi \over 6}}$$
2. B.$${{\pi \over 3}}$$
3. C.$${{\pi \over 8}}$$
4. D.$${{\pi \over 4}}$$