In order to evaluate the tangent function "visually", you have to draw a vertical line tangent to the circle (i.e. the line x=1), and extend the radius until it meets that line.
Since the angle -180° makes you land on point (-1,0), if you extend the radius you'll meet the vertical line at point (1,0).
The tangent is the y-value of this point, and thus it's zero.
