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[math]tan\alpha +tan\beta +tan\gamma =tan\gamma *tan\alpha *tan\beta[/math] where [math]\alpha +\beta +\gamma =180\deg[/math]?
How does that relate to triangles?
The sum of the angles in any triangle is always 180 degrees. So if we define three angles as [math]\alpha[/math], [math]\beta[/math], and [math]\gamma[/math], and they also add up to 180 degrees, then they must be the angles of a triangle.