This Problem Was Made In 2016

Geometry Level 5

{x3+3x2+2019x+2017=sin2θ12y3+3y2+2019y+2017=cos2θ12\begin{cases} x^3+3x^2+2019x+2017=\sin^2\theta - \frac{1}{2} \\ y^3+3y^2+2019y+2017=\cos^2\theta - \frac{1}{2} \end{cases}

Given that xx, yy and θ\theta (measured in radians) are real numbers satisfying the system of equations above, find the value of x+yx+y.

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