Triangle-Ception, Don't Lose Your Count!
Calvin was given 2016 line segments with lengths of \(1, 2, 3, 4,\ldots , 2015, 2016\) respectively and he had to pick three random lines to form a triangle. Determine the possible number of triangles Calvin could form.
Details and assumptions
\(\bullet\) All the lengths are in the same system of units.