From Förberedande kurs i matematik 1

The tangent value of the angle \displaystyle {2\pi }/{7}\; is the gradient of the line which makes an angle \displaystyle {2\pi }/{7}\; with the \displaystyle x -axis.

slope = \displaystyle {\tan 2\pi }/{7}\; FIGURE1 slope = \displaystyle {\tan 2\pi }/{7}\; FIGURE2

From the figure, we see that the angle between \displaystyle {\pi }/{2}\; and \displaystyle 2\pi which gives a line with the same slope as the angle \displaystyle {2\pi }/{7}\; is \displaystyle {v=2\pi }/{7}\;+\pi ={9\pi }/{7}\; .