How do you find two solution to #csc x= (2√3)/3?

To find two solutions to $\csc(x) = \frac{2\sqrt{3}}{3}$, you can follow these steps:

1. Recognize that $\csc(x)$ is the reciprocal of the sine function $\sin(x)$.
2. Rewrite the equation as $\sin(x) = \frac{1}{\csc(x)}$.
3. Since $\csc(x) = \frac{1}{\sin(x)}$, substitute $\frac{2\sqrt{3}}{3}$ for $\csc(x)$ in the equation.
4. Solve the resulting equation $\sin(x) = \frac{3}{2\sqrt{3}}$.

$\sin(x) = \frac{3}{2\sqrt{3}}$

$\sin(x) = \frac{\sqrt{3}}{2}$

Now, recall the values of $\sin(x)$ in the unit circle:

$\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$

$\sin\left(\frac{2\pi}{3}\right) = \frac{\sqrt{3}}{2}$

So, the two solutions to $\csc(x) = \frac{2\sqrt{3}}{3}$ are $x = \frac{\pi}{3}$ and $x = \frac{2\pi}{3}$.