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 $\tan \theta$