Answer
$$\theta=35.26^o.$$
Work Step by Step
\begin{align*}
\cos \theta &=\frac{\langle 1,1,1\rangle \cdot \langle 1,0,1\rangle}{\|\langle 1,1,1\rangle\|\|\langle 1,0,1\rangle\|}\\
&=\frac{1+0+1}{\sqrt{1+1+1}\sqrt{1+0+1}}\\
&=\frac{2}{\sqrt{3}\sqrt{2}}\\
&=\frac{2}{\sqrt{6}}=0.816
\end{align*}
That is $$\theta=\cos^{-1}0.816=35.26^o.$$
