Question Stem for Question Nos. 17 and 18

Consider the ellipses given by $$x^2+4y^2=1$$ and $$4x^2+y^2=1$$.

Let $$P$$ be the point in the first quadrant where the given ellipses intersect. If $$\theta$$ is the acute angle between the tangents to the given ellipses at the point $$P$$, then the value of $$4\tan\theta$$ is ___.