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Spoiler for how about
Using the notation in the link:
1/[d1d2csc(θ1)]+1/[d1d3csc(θ2)]+1/[d2d3csc(θ2-θ1)]
or
sin(θ1)/(d1d2) + sin(θ2)/(d1d2) + sin(θ2 - θ1)/(d2d3)
As the area of the plane approaches infinity one intersection corresponds to one 'block' or 'section' of the grid made by two intersecting sets of parallel lines. So calculating how many of those 'blocks' from each pair of intersecting sets fit into one unit of area I got the above equation.
1/[d1d2csc(θ1)]+1/[d1d3csc(θ2)]+1/[d2d3csc(θ2-θ1)]
or
sin(θ1)/(d1d2) + sin(θ2)/(d1d2) + sin(θ2 - θ1)/(d2d3)
As the area of the plane approaches infinity one intersection corresponds to one 'block' or 'section' of the grid made by two intersecting sets of parallel lines. So calculating how many of those 'blocks' from each pair of intersecting sets fit into one unit of area I got the above equation.
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