Given:
\[\tan A = 3 \cot A \implies \tan A = 3 \times \frac{1}{\tan A}\]
\[\tan^2 A = 3 \implies \tan A = \sqrt{3}\]
For $\tan A = \sqrt{3}$, the corresponding angle is:
\[A = 60^\circ\]
The direction cosines of two lines are connected by the relations \( 1 + m - n = 0 \) and \( lm - 2mn + nl = 0 \). If \( \theta \) is the acute angle between those lines, then \( \cos \theta = \) ?