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Consider the solution of trigonometric equations.
  1. Find all solutions to the equation \(\sin(x) = \frac{\sqrt{2}}{2}\) on the domain \(0 \le x \le 2\pi\).
  2. Hence, find all solutions to the equation \(\sin(2x) = \frac{\sqrt{2}}{2}\) on the domain \(0 \le x \le \pi\).

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