Coterminal angles: are angles in standard position (angles with the initial side on the
positive x-axis) that have a common terminal side.
If we call our angle as θ, its coterminal angles are given by
[tex]\begin{gathered} \theta\pm2\pi n \\ n\in\mathbb{N} \end{gathered}[/tex]
Our angle is 4π/3, therefore, its coterminal angles are
[tex]\begin{gathered} \frac{4\pi}{3}\pm2\pi n=\ldots,\frac{4\pi}{3}-4\pi,\frac{4\pi}{3}-2\pi,\frac{4\pi}{3},\frac{4\pi}{3}+2\pi,\frac{4\pi}{3}+4\pi,\ldots \\ =\ldots,-\frac{8\pi}{3},-\frac{2\pi}{3},\frac{4\pi}{3},\frac{10\pi}{3},\frac{16\pi}{3},\ldots \end{gathered}[/tex]
From the given options, those that fits this description are
[tex]-\frac{8\pi}{3},-\frac{2\pi}{3},\frac{10\pi}{3}[/tex]
