cosπ/7-cos2π/7+cos3π/7
=cosπ/7+cos3π/7+cos5π/7
=(2sinπ/7*cosπ/7+2sinπ/7*cos3π/7+2sinπ/7*cos5π/7)/(2sinπ/7)
=[sin2π/7+(sin4π/7-sin2π/7)+(sin6π/7-sin4π/7)]/(2sinπ/7)
=(sin6π/7)/(2sinπ/7)
=(sinπ/7)/(2sin/π7)
=1/2
=cosπ/3