AHSME 1980 Problem 12

The equations of $L_1$ and $L_2$ are $y=mx$ and $y=nx$, respectively. Suppose $L_1$ makes twice as large of an angle with the horizontal (measured counterclockwise from the positive x-axis ) as does $L_2$, and that $L_1$ has 4 times the slope of $L_2$. If $L_1$ is not horizontal, then $mn$ is $\text{(A)} \ \frac{\sqrt{2}}{2} \text{(B)} \ -\frac{\sqrt{2}}{2} \text{(C)} \ 2 \text{(D)} \ -2 \text{(E)} \ \text{not uniquely determined}$