If √ 3sin α + cos α = 2 / 3, then cos (2 α + π / 3) is equal to

√3sinα+cosα=2/3,
2*[(√3/2)sinα+(1/2)cosα]=2*(1/3),
2*sin(π/6+α)=2*(1/3)
sin(π/6+α)=1/3
cos(π/3+2α)=1-2[sin(π/6+α)]^2=1-2/9=7/9

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