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$Cos \frac{5 \pi }{7}=Cos( \pi - \frac{2 \pi }{7})=-Cos \frac{2 \pi }{7}$
Умножим и разделим на
$8Sin \frac{ \pi }{7} \\\\ -\frac{8Sin \frac{ \pi }{7} Cos \frac{ \pi }{7}Cos \frac{2 \pi }{7}Cos \frac{4 \pi }{7} }{8Sin \frac{ \pi }{7} } =- \frac{4Sin \frac{2 \pi }{7}Cos \frac{2 \pi }{7} Cos \frac{4 \pi }{7} }{8Sin \frac{ \pi }{7} }=- \frac{2Sin \frac{4 \pi }{7} Cos \frac{4 \pi }{7} }{8Sin \frac{ \pi }{7} } =$ $=- \frac{Sin \frac{8 \pi}{7} }{8Sin \frac{ \pi }{7} }=- \frac{Sin( \pi + \frac{ \pi }{7} )}{8Sin \frac{ \pi }{7} } = \frac{Sin \frac{ \pi }{7} }{8Sin \frac{ \pi }{7} }= \frac{1}{8}$

$\frac{8Sin \frac{2 \pi }{7}*Cos \frac{2 \pi }{7} Cos \frac{4 \pi }{7} Cos \frac{8 \pi }{7} }{8Sin \frac{2 \pi }{7} } = \frac{4Sin \frac{4 \pi }{7}Cos \frac{4 \pi }{7} Cos \frac{8 \pi }{7} }{8Sin \frac{2 \pi }{7} } = \frac{2Sin \frac{8 \pi }{7}Cos \frac{8 \pi }{7} }{8Sin \frac{2 \pi }{7} }= \frac{Sin \frac{16 \pi }{7} }{8Sin \frac{2 \pi }{7} }$ $= \frac{Sin(2 \pi + \frac{2 \pi }{7} )}{8Sin \frac{2 \pi }{7} } = \frac{Sin \frac{2 \pi }{7} }{8Sin \frac{2 \pi }{7} } = \frac{1}{8}$