The value of \( \int_{0}^{\frac{3 \pi}{2}} \frac{\left|\tan ^{-1} \...

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The value of \( \int_{0}^{\frac{3 \pi}{2}} \frac{\left|\tan ^{-1} \tan x\right|-\left|\sin ^{-1} \sin x\right|}{\left|\tan ^{-1} \tan x\right|+\left|\sin ^{-1} \sin x\right|} d x \) is equal
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