1.

: ( 1 + \operatorname { cos } \frac { \pi } { 8 } ) ( 1 + \operatorname { cos } \frac { 3 \pi } { 8 } ) ( 1 + \operatorname { cos } \frac { 5 \pi } { 8 } ) ( 1 + \operatorname { cos } \frac { 7 \pi } { 8 } ) = \frac { 1 } { 8 }

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