Ellipse

Consider the ellipses given by

\(x^2+4 y^2=1 \quad \text { and } \quad 4 x^2+y^2=1\)

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 $\_\_\_\_$ .