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Evaluate the definite integral: $y(x) = \int_{0}^{\pi} \sin(x+y(x)) dx$

We were recently asked to evaluate this - $y(x) = \int_{0}^{\pi} \sin(x+y(x)) dx$ I think we can start by breaking up the integral as $y(x) = \int_{0}^{\pi} \sin(x)\cos(y(x)) dx + \int_{0}^{\pi} ...