Find the acute angle from line directions

Let θ be the angle between $(1,2,1)$ and $(3,2,6)$. The dot-product equation is $(1,2,1)\cdot(3,2,6)=|(1,2,1)||(3,2,6)|\cos\theta$. Their dot product is $3+4+6=13$ and their magnitudes are $\sqrt6$ and 7, so $13=7\sqrt6\cos\theta$.

$\theta=\cos^{-1}(13/(7\sqrt6))=40.69639\ldots^\circ$. This is already acute, so the angle between the lines is $40.7^\circ$ to 1 decimal place, or 0.710 rad to 3 significant figures.