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Within the interval (0, π), how many solutions exist for the equation sin(x) + 2sin(2x) − sin(3x) = 3?

1. An infinite number of solutions
2. Exactly three solutions
3. Only one solution
4. No solutions

Correct answer: No solutions

Solution

The maximum value of sin(x) + 2sin(2x) − sin(3x) is less than 3 within the interval (0, π). Therefore, the equation cannot equal 3, and no solutions exist.

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