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sin(theta - alpha), sin theta, sin(theta + alpha) in H.P.: find cos^2 theta

The same question, asked 2 times: 3 May 2023 S2*, 14 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S2

    125
    If sin⁡(θ−α), sin⁡θ\sin(\theta-\alpha),\,\sin\theta and sin⁡(θ+α)\sin(\theta+\alpha) are in H.P., then the value of cos⁡2θ\cos^{2}\theta is

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  2. Question 2

    14 May 2024 S1

    144
    If sin⁡(θ−α)\sin(\theta-\alpha), sin⁡θ\sin\theta and sin⁡(θ+α)\sin(\theta+\alpha) are in H.P., then the value of cos⁡2θ\cos2\theta is

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