1. For which natural values of $a$ does the equation $\gcd(4|\cos x|, a|\cos 3x|)=2$ have solutions? Find these solutions.
$$
\left[\begin{array}{l}
a=4 n-2, n \in N ; x=\frac{\pi k}{3}, k \in Z \\
a=4 n, n \in N ; x= \pm \frac{\pi}{3}+\pi k, k \in Z
\end{array}\right.
$$