8.028. $2 \operatorname{tg}^{3} x-2 \operatorname{tg}^{2} x+3 \operatorname{tg} x-3=0$.

8.028. $2 \tan^{3} x-2 \tan^{2} x+3 \tan x-3=0$.
## Solution.

Domain of definition: $\cos x \neq 0$.

From the condition $2 \operatorname{tg}^{2} x(\operatorname{tg} x-1)+3(\operatorname{tg} x-1)=0, \quad(\operatorname{tg} x-1)\left(2 \operatorname{tg}^{2} x+3\right)=0$.

Hence $\operatorname{tg} x-1=0, \operatorname{tg} x=1, x=\frac{\pi}{4}+\pi n=\frac{\pi}{4}(4 n+1), n \in Z$.

Answer: $\quad x=\frac{\pi}{4}(4 n+1), \quad n \in Z$.