`int_0^(pi/4)2tan^3xdx=1-log2`

Explanation

To solve the integral \( \int_0^{\frac{\pi}{4}} 2 \tan^3 x \, dx \) and show that it equals \( 1 - \log 2 \), we can follow these steps:

### Step 1: Set up the integral
Let:
\[ I = \int_0^{\frac{\pi}{4}} 2 \tan^3 x \, dx \]

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