A little help with reference angles.

So this is from a calculus problem but I'm not sure how to achieve the other angle (240 degrees). I know you get the (120 degrees from reference angle (180-60 = 120) but for 240 I'm not sure. Thanks and heres the problem.

$\displaystyle 2\cos t+1=0\Longrightarrow \cos t = -\frac{1}{2}\Longrightarrow

t=\left\{\begin{array}{c}\frac{2\pi}{3}\\{}\\\frac {4\pi}{3}\end{array}\right.\,+2\pi

k\,,\,\,k\in\mathbb{Z}

$

How would I go about achieving the $\displaystyle \frac {4 \pi} 3 $ ?

Thanks.