ANSWER
[tex] - \frac{16 \pi}{5} \: and \: \frac{14\pi}{5}[/tex]
EXPLANATION
Coterminal angles are angles in standard position that have the same terminal side.
To find an angle in standard position that is coterminal with
[tex] - \frac{6 \pi}{5} [/tex]
We add or subtract multiples of
[tex]2 \pi[/tex]
The first addition gives,
[tex] - \frac{6 \pi}{5} + 2 \pi = \frac{4 \pi}{5} [/tex]
We add the second multiple to get,
[tex] - \frac{6 \pi}{5} +2( 2 \pi )= \frac{14 \pi}{5} [/tex]
Since this is the maximum value among the options, we end the addition here.
Let us now subtract the first multiple to get,
[tex] - \frac{6 \pi}{5} - 2 \pi = - \frac{16 \pi}{5} [/tex]
We end the subtraction here because this is the least value among the options.
Therefore the angles that are coterminal with
[tex] - \frac{6 \pi}{5} [/tex]
are
[tex] - \frac{16 \pi}{5} \: and \: \frac{14\pi}{5}[/tex]
