3.3.1. (12 points) Simplify the expression

$$
\left(\frac{2}{\sqrt[3]{3}}+3\right)-\left(\frac{\sqrt[3]{3}+1}{2}-\frac{1}{\sqrt[3]{9}+\sqrt[3]{3}+1}-\frac{2}{1-\sqrt[3]{3}}\right): \frac{3+\sqrt[3]{9}+2 \sqrt[3]{3}}{2}
$$

Answer: 3.
Solution. Let's introduce the notation $a=\sqrt[3]{3}$. Then the expression transforms to

$$
\left(\frac{2}{a}+3\right)-\left(\frac{a+1}{a^{3}-1}-\frac{1}{a^{2}+a+1}-\frac{2}{1-a}\right): \frac{a^{3}+a^{2}+2 a}{a^{3}-1}
$$

and after simplifications and performing the division, it transforms to $\left(\frac{2}{a}+3\right)-\frac{2}{a}$.