Answer
$$\theta=\cos^{-1}\frac{4}{\sqrt{30}}.$$
Work Step by Step
\begin{align*}
\cos \theta &=\frac{\langle 3,0,1\rangle \cdot \langle 1,1,1\rangle}{\|\langle 3,0,1\rangle\|\|\langle 1,1,1\rangle\|}\\
&=\frac{3+0+1}{\sqrt{9+0+1}\sqrt{1+1+1}}\\
&=\frac{4}{\sqrt{10}\sqrt{3}}\\
&=\frac{4}{\sqrt{30}}
\end{align*}
That is $$\theta=\cos^{-1}\frac{4}{\sqrt{30}}.$$
