Answer
$$\theta=65.49^o.$$
Work Step by Step
Since $ n_1=\langle 2,3,7\rangle $ and $ n_2=\langle 4,-2,2\rangle $, then we have
\begin{align*}
\cos \theta &=\frac{n_1 \cdot n_2}{\|n_1\|\|n_2\|}\\
&=\frac{8-6+14}{\sqrt{4+9+49}\sqrt{16+4+4}}\\
&=\frac{16}{\sqrt{62}\sqrt{24}}.
\end{align*}
That is $$\theta=65.49^o.$$
