$\int_0^{\pi/4} \log\bigl(1 - \tfrac{1}{4\cos^2\theta}\bigr)\,d\theta = -G/3$, $G$ Catalan's constant

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$\int_0^{\pi/4} \log\bigl(1 - \tfrac{1}{4\cos^2\theta}\bigr)\,d\theta = -G/3$, $G$ Catalan's constant · Prove2Me