We can read #sqrt3# as #sqrt3/1# because tan is the ratio of two sides. The special triangle which has these sides is a right-angled triangle with sides in the ratio #1 : 2 : sqrt3# and angles of 30° and 60°.
#tan 60° = sqrt3/1#
However we are dealing with a negative #sqrt3#
From #0° to 360°# Tan values are negative in the second and fourth quadrants.
#theta = 180°-60° = 120°" or "theta = 360-60 = 300°#
Any angle from #120°# which is a rotation through 180° will be such that #Tan theta = -sqrt3#
Hence #theta = 120° + 180n#
