Find the value of sin^2 pi/10 + sin^2 4pi/10 + sin^2 6pi/10 + sin^2 9pi/10.

We have,sin2π10+sin24π10+sin26π10+sin29π10=sin2π10+sin24π10+sin2π-4π10+sin2π-π10=sin2π10+sin24π10+sin24π10+sin2π10        sin2π-θ=sin2θ=2sin2π10+2sin24π10=2sin2π10+2sin2π2-π10=2sin2π10+2cos2π10           sin2π2-θ=cos2θ=2sin2π10+cos2π10=2×1           sin2θ+cos2θ=1=2     

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