The expression in the image involves nested trigonometric functions. It appears as follows:

$\sin \left[ \tan^{-1} \left( \frac{2x}{1 - x^2} \right) + \tan^{-1} \left( \frac{8x}{1 - 16x^2} \right) + \tan^{-1} \left( \frac{3x}{1 - 9x^2} \right) \right]$

Would you like to solve this step by step or need more details on any specific part?

Here are some related questions to explore:

1. What is the formula for simplifying sums of inverse tangent (arctan) functions?
2. How can we simplify expressions involving nested trigonometric identities?
3. What is the domain of this trigonometric function?
4. How does the sine function behave with sum of angles?
5. Can we use substitution to simplify this type of expression?

Tip: When dealing with sums of inverse tangent functions, you can use the identity: $\tan^{-1} a + \tan^{-1} b = \tan^{-1} \left( \frac{a + b}{1 - ab} \right) \quad \text{if} \quad ab < 1.$