f(x)=sin(2x+π/3)+sin(2x-π/3)+2cos^2x
=2sin[(2x+π/3+2x-π/3)/2]cos[(2x+π/3-2x+π/3)/2]+cos2x+1
=2sin(2x)cosπ/3+cos2x+1
=sin2x+cos2x+1
=√2(√2/2sin2x+√2/2cos2x)+1
=√2sin(2x+π/4)+1
∴最小正周期T=2π/2=π
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