+500 secant = 1/cos
Dividing by -sqrt3 on both sides
\(\sec{\theta} = -\frac2{\sqrt3}\)
Rationalizing the denominator by multiplying it by sqrt3/sqrt3(which is one):
\(\sec{\theta} = -2\sqrt{3}/3\)
Substituting in 1/cos:
\(1/\cos{\theta} = -2\sqrt{3}/3\)
\(\cos{\theta} = -3/2\sqrt{3}\)
Rationalizing like before by multiplying by sqrt3 / sqrt 3, we get:
\(\cos{\theta} = -3\sqrt{3}/6 = -\sqrt3/2\)
The values for which this is true between [0, 2pi] are :
\(\cos{5\pi/6}\) radians (cos 150 degrees) and \(\cos{7\pi/6} \)(cos 210 degrees). The general forms for these are then indeed your answer because the period of cosine is 2pi.
