Answer
$$\theta= 120^o.$$
Work Step by Step
\begin{align*}
\cos \theta &=\frac{\langle 0,1,1\rangle \cdot \langle1,-1,0\rangle}{\|\langle 0,1,1\rangle\|\|\langle 1,-1,0\rangle\|}\\
&=\frac{0-1+0}{\sqrt{0+1+1}\sqrt{1+1+0}}\\
&=\frac{-1}{\sqrt{2}\sqrt{2}}\\
&=-\frac{1}{2}.
\end{align*}
That is $$\theta=\cos^{-1}(-\frac{1}{2})=120^o.$$
