Find the exact angular measurement $\theta$ between the following pair of spatial lines in three-dimensional space:
\[
\frac{x-2}{3} = \frac{y+5}{2} = \frac{1-z}{-6} \quad \text{and} \quad \frac{x-7}{1} = \frac{y}{2} = \frac{6-z}{-2}
\]
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Always look out for terms like $1-z$ or $3-x$ in line equations. Forgetting to rearrange them to standard form will change the sign of your direction numbers and result in an incorrect angle calculation.