Use the following useful fact.Originally Posted bykingkaisai2

, where is the angle between these two vectors.

Select any two point on L1, say

Then you get,

The vector between these two points is (in any order),

For the other line L2, select two point to draw a vector say,

Then you get,

The vector between these two points is,

Now do the calculations.

As a result, you have,

Thus,

Thus,

Thus,

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My solution is based on the following observation: the angles between two lines is the same as the angles between any two vectors on these two lines.