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tan^-1((1-x)/(1+x)) = (1/2) tan^-1 x: find x

The same question, asked 2 times: May 2022 S1, 12 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    May 2022 S1

    102
    If tan⁡−1 ⁣(1−x1+x)=12tan⁡−1x\tan^{-1}\!\left(\frac{1-x}{1+x}\right) = \frac{1}{2}\tan^{-1} x, then xx has the value

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  2. Question 2

    12 May 2024 S2

    116
    If tan⁡−1 ⁣(1−x1+x)=12tan⁡−1x\tan^{-1}\!\left(\frac{1-x}{1+x}\right) = \frac{1}{2}\tan^{-1}x, then xx is

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