An equation can be solved by tracing its values from the graph
The solutions in increasing order are: [tex]-\frac{2\pi}3, -\frac{\pi}3, \frac{4\pi}3[/tex] and [tex]\frac{5\pi}3[/tex]
The equation is given as:
[tex]\csc(x) = -\frac{2\sqrt 3}{3}[/tex]
Within the interval [tex][-2\pi, 2\pi][/tex]
The graph of [tex]\csc(x) = -\frac{2\sqrt 3}{3}[/tex] is missing from the question, so I added it as an attachment.
From the attached graph,
Within the interval [tex][-2\pi, 2\pi][/tex], the values of x for which [tex]\csc(x) = -\frac{2\sqrt 3}{3}[/tex] are:
[tex]x_1 = -\frac{2\pi}3[/tex]
[tex]x_2 = -\frac{\pi}3[/tex]
[tex]x_3 = \frac{4\pi}3[/tex]
[tex]x_2 = \frac{5\pi}3[/tex]
So, we can conclude that:
In increasing order from left to right, the values of x are:
[tex]-\frac{2\pi}3, -\frac{\pi}3, \frac{4\pi}3[/tex] and [tex]\frac{5\pi}3[/tex]
Read more about graphs at:
https://brainly.com/question/2285028
