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Geometry Level 3

What is the sum of all x[0,π]x \in [0,\pi ] which satisfy this equation?

sinx+12cosx=sin2(x+π4)\sin{x}+\frac { 1 }{ 2 } \cos{x}={ \sin }^{ 2 }\left(x+\frac { \pi }{ 4 }\right)

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