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Cos x is negative in (π/2 , π) . So near 2π/3  on both sides, at 2π/3 +- delta
Sin x is positive. in this domain.

so in this domain  y =  - cos x + sin x
differentiating dy/dx = sin x + cos x
At  2π/3 , dy/dx  is  sin 2π/3 + cos 2π/3 = √3/2 - 1/2  = (√3 -1 )/2

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