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Suppose the lines make angles θ1 and θ2 with the X-axis, and let θ be the angle between them. Using some basic geometry, one can tell that the angle between the lines (θ) will be θ1 - θ2.
Then tanθ = tan(θ1 - θ2), which leads to tanθ = tanθ1−tanθ21+tanθ1tanθ2.
Now, replacing tanθ1 and tanθ2 by m1 and m2 respectively, we get tanθ =
m1−m21+m1m2m1−m21+m1m2m1−m21+m1m
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