Answer
$$\theta=\cos^{-1}\frac{1}{\sqrt{10}}.$$
Work Step by Step
\begin{align*}
\cos \theta &=\frac{\langle 1,1,0\rangle \cdot \langle 0,1,2\rangle}{\|\langle 1,1,0\rangle\|\|\langle 0,1,2\rangle\|}\\
&=\frac{0+1+0}{\sqrt{1+1+0}\sqrt{0+1+4}}\\
&=\frac{1}{\sqrt{2}\sqrt{5}}\\
&=\frac{1}{\sqrt{10}}
\end{align*}
That is $$\theta=\cos^{-1}\frac{1}{\sqrt{10}}.$$
