okay so I get that I factor it out with difference of two squares

(sec theta - 2)(sec theta +2)=0

so

sec theta = 2

sec theta= -2

therefore

cos theta = 1/2 = pi/3 which gives me the solutions: (pi/3 + 2pi N) and (2pi/3 + 2pi N)

what I don't understand is this...since cos theta also = -1/2 shouldn't the solutions also include

(4pi/3+2pi N) and (5pi/3 + 2pi N)?