How to solve this?

cos 2pi/7 +cos 4pi/7 +cos 6pi/7 =?

cos2π7+cos4π7+cos6π7
Multiply and divide by sinπ7we have;
sinπ7cos2π7+sinπ7cos4π7+sinπ7cos6π7sinπ7
Convert from product to sum using the rule 2sinAcosB=sinA-B+sinA+B we have;
=sinπ7-2π7+sinπ7+2π7+sinπ7-4π7+sinπ7+4π7+sinπ7-6π7+sinπ7+6π72sinπ7=sin-π7+sin3π7+sin-3π7+sin5π7+sin-5π7+sin7π72sinπ7=sin-π7+sinπ2sinπ7=sin-π7+02sinπ7=-12

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