Answer
$$\theta=\pi.$$
Work Step by Step
\begin{align*}
\cos \theta &=\frac{v \cdot w}{\|v\|\|w\|}\\
&=\frac{-\|v\|\|w\|}{\|v\|\|w\|}\\
&=-1.
\end{align*}
That is $$\theta=\pi.$$
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