Answer
$$\theta=75.75^o.$$
Work Step by Step
\begin{align*}
\cos \theta &=\frac{\langle 3,1,1\rangle \cdot \langle 2,-4,2\rangle}{\|\langle 3,1,1\rangle\|\|\langle 2,-4,2\rangle\|}\\
&=\frac{6-4+2}{\sqrt{9+1+1}\sqrt{4+16+4}}\\
&=\frac{4}{\sqrt{11}\sqrt{24}}\\
&=0.246.
\end{align*}
That is $$\theta=\cos^{-1}0.246=75.75^o.$$
