求sin2/7π+sin3/7π-sinπ/7的值

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求sin2/7π+sin3/7π-sinπ/7的值
（根号7）/2,怎么算的

sin（2π/7）+sin（3π/7）-sin（π/7）=sin(5π/14-π/14)+sin(5π/14+π/14)-sinπ/7
=sin5π/14cosπ/14-cos5π/14sinπ/14+sin5π/14cosπ/14+cos5π/14sinπ/14-sinπ/7
=2sin5π/14cosπ/14-sinπ/7
=2cos(2π/14)cos(π/14)-sin(π/7)=2sin(π/14)cos(π/14)cos(2π/14)/sin(π/14)-sin(π/7)
=sin(2π/14)cos(2π/14)/sin(π/14)-sin(π/7)=(1/2)sin(4π/14)/sin(π/14)-sin(π/7)
=(1/2)sin(2π/7)/sin(π/14)-sin(π/7)=(1/2)sin(2π/7)/cos(6π/14)-sin(π/7)
=(-1/2)sin(2π/7)/cos(2π/7)-sin(π/7)

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