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

$$
1+\cos ^{2}\left(\frac{\pi \sin 2 x}{\sqrt{3}}\right)+\sin ^{2}(2 \sqrt{3} \pi \cos x)
$$

take its smallest possible value?
Answer: $x= \pm \frac{\pi}{6}+\pi k, k \in Z$.