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Set of x >= 0 with tan^-1(2x) + tan^-1(3x) = pi/4: empty, singleton or more

The same question, asked 3 times: 2 May 2023 S1*, 4 May 2023 S1*, 10 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S1

    106
    Considering only the principal values of inverse function, the set A={x≥0 | tan⁡−1(2x)+tan⁡−1(3x)=π4}A = \left\{x \ge 0\,\middle|\, \tan^{-1}(2x) + \tan^{-1}(3x) = \frac{\pi}{4}\right\}

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  2. Question 2

    4 May 2023 S1

    124
    Considering only the Principal values of inverse functions, the set A={x≥0∣tan⁡−1(2x)+tan⁡−1(3x)=π4}A = \{x\geq0 \mid \tan^{-1}(2x)+\tan^{-1}(3x)=\frac{\pi}{4}\}

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  3. Question 3

    10 May 2024 S1

    137
    Set A={x≥0∣tan⁡−1x+tan⁡−1(6x)=π4}A=\{x\ge0\mid\tan^{-1}x+\tan^{-1}(6x)=\frac{\pi}{4}\}

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