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 $\tan\theta$
A $\frac{1}{2}$
B $2$
C $\frac{\sqrt{2}}{2}$
D $\sqrt{2}$
E $\frac{\sqrt{6}}{2}$
F $\frac{\sqrt{6}}{3}$
G $\frac{\sqrt{3}}{3}$
H $\sqrt{3}$