Тригонометрия. Найти значение выражения! [latex]cos \frac{2pi}{7} + cos\frac{4pi}{7} +cos \frac{6pi}{7} [/latex]

sin(α+β) +sin(α-β) =2sinα*cosβ⇔ sinα*cosβ = (1/2)*(sin(α+β) +sin(α-β) ). ---------- cos2π/7 +cos4π/7+ cos6π/7 =2sinπ/7*(cos2π/7 +cos4π/7+ cos6π/7)/2sinπ/7= (2sinπ/7*cos2π/7 +2sinπ/7*cos4π/7+ 2sinπ/7*cos6π/7)/2sinπ/7= (sin3π/7 -sinπ/7 +sin5π/7-sin3π/7+sinπ -sin5π/7) / 2sinπ/7 =  -(sinπ/7) / 2sinπ/7 = -1/2.