##arctan(1/sqrt(3)) = pi/6 or 30^o##

This ratio is one of the standard trigonometric triangles:

##arctan## must provide an angle in quadrants one or four; in quadrant four, the argument would have needed to be negative.

The ratio ## ((1/2))/((sqrt(3)/2)) = 1/sqrt(3)## ##color(white)(“XXXX”)##is that of a ##pi/6## angle (as indicated above).