$4.66 \sin \left(\frac{5 \pi}{2}+4 \alpha\right)-\sin ^{6}\left(\frac{5 \pi}{2}+2 \alpha\right)+\cos ^{6}\left(\frac{7 \pi}{2}-2 \alpha\right)$.

Transform into a product (4.67-4.73):

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4.66 Instruction. Use reduction formulas, as well as the formula for the difference of cubes.

Answer: $\quad \frac{1}{8} \sin 4 \alpha \sin 8 \alpha$.