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About the integral $\int\arctan\left(\frac{1}{\sinh^2 x}\right)dx$, some idea or feedback

While I was playing with Wolfram Alpha calculator I wondered if it is known a closed-form for $$\int_0^\infty\arctan\left(\frac{1}{\sinh^2 x}\right)dx.\tag{1}$$ Wolfram Alpha provide me the ...
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