Why is tangent of 2pi/3 = negative radical 3?
On the unit circle, 2pi/3 is in quadrant two. The triangle has a cosine horizontal leg of -1/2. The sine vertical leg is rt3/2. When you do tangent, it's rt3/2 / -1/2. Mult by the reciprocal and you get rt3/2 x -2/1. That reduces to -rt3