The equation in the image is:

$\frac{\sqrt{x + 8} \cdot \ln{(x^2 - 1)} - \left(\frac{3x^2 - \frac{2x - 8}{x}}{x}\right)}{\cos^{-1}\left(\frac{2x - 3}{x + 1}\right) + \sin{\left(\frac{2\pi}{3x + 2}\right)}} = \frac{\pi}{3}$

Would you like a detailed solution or explanation on how to solve this equation? If so, please specify any part of the equation you'd like to focus on.

Here are 5 questions related to the equation:

1. What is the domain of the function $\ln{(x^2 - 1)}$?
2. How do you simplify the expression $\frac{3x^2 - \frac{2x - 8}{x}}{x}$?
3. What are the principal values for $\cos^{-1}(x)$ and $\sin(x)$?
4. How would you approach solving this equation for $x$?
5. What techniques can be used to simplify the expression before solving?

Tip: When solving equations with logarithmic, trigonometric, and square root functions, it's crucial to consider the domain of each function to avoid invalid solutions.