Let \(\theta\) be the acute angle between the tangents to the ellipse \(\frac{{x}^{2}}{9}+\frac{{y}^{2}}{1}=1\) and the …

Let \(\theta\) be the acute angle between the tangents to the ellipse \(\frac{{x}^{2}}{9}+\frac{{y}^{2}}{1}=1\) and the circle \({x}^{2}+{y}^{2}=3\) at their point of intersection in the first quadrant. The \(\tan \theta\) is equal to:

[JEE Main 2021, 1 Sep (Shift 2)]