3. For what values of $x$ does the expression

$$
4+\operatorname{tg}^{2}(2 \pi \sin \pi x)+\operatorname{ctg}^{2}(3 \pi \cos 2 \pi x)
$$

take its smallest possible value
Answer: $x= \pm \frac{1}{6}+2 m, x= \pm \frac{5}{6}+2 m, m \in Z$.