\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A curve is defined by the implicit equation \(x^3 + \sin(y) = xy\).
  1. Show that \(\dfrac{dy}{dx} = \dfrac{y-3x^2}{\cos(y)-x}\).
  2. Find the slope of the tangent to the curve at the point \((0, \pi)\).

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