theta = 210
which is in the 3rd quadrant (180 < theta < 270)
sec theta = 1 / cos theta
cos 210 = -sqrt(3)/2
so sec theta = -2/sqrt(3)
Cos theta = -sqrt(3)/2, so sec (theta) = 1/cos(theta) = 1/[-sqrt(3)/2] = 2/sqrt(3)
Then rationalize by sqrt(3) to obtain [2 * sqrt(3)]/3
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Verified answer
theta = 210
which is in the 3rd quadrant (180 < theta < 270)
sec theta = 1 / cos theta
cos 210 = -sqrt(3)/2
so sec theta = -2/sqrt(3)
Cos theta = -sqrt(3)/2, so sec (theta) = 1/cos(theta) = 1/[-sqrt(3)/2] = 2/sqrt(3)
Then rationalize by sqrt(3) to obtain [2 * sqrt(3)]/3