1980 AHSME 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} \qquad \text{(B)} \ -\frac{\sqrt{2}}{2} \qquad \text{(C)} \ 2 \qquad \text{(D)} \ -2 \qquad \text{(E)} \ \text{not uniquely determined}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.