12.5.15 Olympic algebra

Condition: Find all values ​​of the variable \( x \), for each of which both expressions \[ \begin{array}{l} f(x)=\tan ^{2}\left(\frac{\pi \cos x}{2 \sqrt{2}}\right)+\cot ^{2}\left(\frac{\pi \cos x}{2 \sqrt{2}}\right) \\ \text { and } g(x)=\frac{\sqrt{15-2 x-x^{2}}+2 x+4}{2+x} \end{array} \] are defined, and the value of the smaller of the expressions does not exceed two (if two numbers are equal, then any of them is considered smaller).