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Sum of the solutions in [0, 2pi] common to 2 sin^2 theta = cos 2theta and 2 cos^2 theta + 3 sin theta = 0

The same question, asked 2 times: 26 Jul 2022, 22 Jan 2025. Every wording below, oldest first.

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  1. Question 1

    26 Jul 2022

    175
    If the sum of solutions of the system of equations 2sin⁡2θ−cos⁡2θ=02\sin^{2}\theta - \cos2\theta = 0 and 2cos⁡2θ+3sin⁡θ=02\cos^{2}\theta + 3\sin\theta = 0 in the interval [0,2π]\lbrack 0,2\pi\rbrack is kπk\pi, then kk is equal to

  2. Question 2

    22 Jan 2025

    143
    The sum of all values of θ∈[0,2π]\theta \in \lbrack 0,2\pi\rbrack satisfying 2sin⁡2θ=cos⁡2θ2\sin^{2}\theta = \cos2\theta and 2cos⁡2θ=3sin⁡θ2\cos^{2}\theta = 3\sin\theta is

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