examday

/TMUA

The circle $C_1$ has equation $(x+2)^2+(y-1)^2=3$.

The circle $C_2$ has equation $(x-4)^2+(y-1)^2=3$.

The straight line $l$ is a tangent to both $C_1$ and $C_2$ and has positive gradient.

The acute angle between $l$ and the $x$-axis is $\theta$.

Find the value of $\tan\theta$.