Coordinate Geometry: JEE Main 2021 Mathematics 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 :