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Let \(f\) be the function defined by:$$ f(x) = \dfrac{2}{\sin(x) + 3} $$
  1. Justify that \(f\) is defined for all \(x \in \mathbb{R}\).
  2. Calculate the derivative \(f'(x)\).
  3. Deduce the variations of \(f\) on the interval \([-\pi, \pi]\).

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