解：由誘導公式可得：cos6π/7=-cosπ/7； cosπ/7=-cos6π/7,cos3π/7=-cos4π/7,cos5π/7=-cos2π/7 ∴ cos2π/7cos4π/7cos6π/7 =-cosπ/7cos2π/7cos4π/7 =-sinπ/7cosπ/7cos2π/7cos4π/7/sinπ/7 =-1/2·sin2π/7cos2π/7cos4π/7/sinπ/7 =-1/4·sin4π/7cos4π/7/sinπ/7 =-1/8·sin8π/7/sinπ/7 =-1/8·(-sinπ/7)/sinπ/7 =1/8 而cosπ/7cos3π/7cos5π/7=(-cos6π/7)(-cos4π/7)(-cos2π/7) =-cos2π/7cos4π/7cos6π/7=-1/8 ∴原式=-1/64