向量 $\boldsymbol{a}$，$\boldsymbol{b}$ 满足 $\left(\boldsymbol{a} - \boldsymbol{b}\right) \cdot \left(2\boldsymbol{a} + \boldsymbol{b}\right) = -4$，且 $|\boldsymbol{a}| = 2$，$\left|\boldsymbol{b}\right| = 4$，则 $\boldsymbol{a}$ 与 $\boldsymbol{b}$ 夹角的余弦值等于______.