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Number of solutions of a quadratic in sin x over several periods

The same question, asked 2 times: 16 May 2023 S1*, 25 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    16 May 2023 S1

    128
    The number of values of x in the interval (0,5π)(0, 5\pi) satisfying the equation 3sin⁡2x−7sin⁡x+2=03\sin^2 x - 7\sin x + 2 = 0

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  2. Question 2

    25 Apr 2025 S1

    132
    The number of values of xx in the interval [0,3π]\lbrack 0,3\pi\rbrack satisfying the equation 2sin⁡2x+5sin⁡x−3=02\sin^{2}x+ 5\sin x- 3 = 0 is

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