4. If
$$
\sin x \cdot \sin 2 x \cdot \sin 3 x+\cos x \cdot \cos 2 x \cdot \cos 3 x=1 \text {, }
$$

then $x=$ $\qquad$ .
4. $k \pi(k \in \mathbf{Z})$.
$$
\begin{array}{l}
\text { Given } 1=|\sin x \cdot \sin 2 x \cdot \sin 3 x+\cos x \cdot \cos 2 x \cdot \cos 3 x| \\
\leqslant|\sin x \cdot \sin 2 x \cdot \sin 3 x|+|\cos x \cdot \cos 2 x \cdot \cos 3 x| \\
\leqslant|\sin x \cdot \sin 2 x|+|\cos x \cdot \cos 2 x| \\
\leqslant \max \{|\cos x|,|\cos 3 x|\} \leqslant 1 \\
\Rightarrow|\cos x|=1 \text { or }|\cos 3 x|=1 . \\
\text { If }|\cos 3 x|=1 \text {, then } \\
\sin 3 x=0 \Rightarrow|\cos x|=1 .
\end{array}
$$

From $|\cos x|=1$, we get $x=k \pi(k \in \mathbf{Z})$.
Upon verification, $x=k \pi(k \in \mathbf{Z})$ satisfies the original equation.