If sin4$\alpha $ + 4 cos4$\beta $ + 2 = 4$\sqrt 2 $ sin $\alpha $ cos $\beta $; $\alpha $, $\beta $ $ \in $ [0, $\pi $], then cos($\alpha $ + $\beta $) $-$ cos($\alpha $ $-$ $\beta $) is equal to :

Question

If sin⁴$\alpha $ + 4 cos⁴$\beta $ + 2 = 4$\sqrt 2 $ sin $\alpha $ cos $\beta $; $\alpha $, $\beta $ $ \in $ [0, $\pi $],
then cos($\alpha $ + $\beta $) $-$ cos($\alpha $ $-$ $\beta $) is equal to :

$ - \sqrt 2 $