8. In $\triangle A B C$ and $\triangle A E F$, $B$ is the midpoint of $E F$, $A B=E F=1, B C=6, C A=\sqrt{33}$, if $\overrightarrow{A B} \cdot \overrightarrow{A E}+\overrightarrow{A C} \cdot \overrightarrow{A F}=2$, then the cosine value of the angle between $\overrightarrow{E F}$ and $\overrightarrow{B C}$ is $\qquad$ .
$$
\begin{array}{l}
\overrightarrow{A B} \cdot \overrightarrow{A E}+\overrightarrow{A C} \cdot \overrightarrow{A F}=\overrightarrow{A B}(\overrightarrow{A E}+\overrightarrow{A F})+\overrightarrow{B C} \cdot \overrightarrow{A F}=2 \overrightarrow{A B}^{2}+\overrightarrow{B C} \cdot \overrightarrow{A F}=2 \\
\Rightarrow \overrightarrow{B C} \cdot \overrightarrow{A F}=0 \Rightarrow B C \perp A F . \text{ Let } B C \text{ intersect } A F \text{ at point } D, \text{ in } \triangle A B C, \\
\cos \angle A B C=\frac{1+36-33}{2 \cdot 1 \cdot 6}=\frac{1}{3}=B D \Rightarrow \cos \langle\overrightarrow{E F}, \overrightarrow{B C}\rangle=\frac{B D}{B F}=\frac{2}{3} .
\end{array}
$$

So the cosine of the angle between $\overrightarrow{E F}$ and $\overrightarrow{B C}$ is $\frac{2}{3}$.