Evaluate `int_(0)^(pi//2)lnsin2xdx`

Explanation

To evaluate the integral \( I = \int_{0}^{\frac{\pi}{2}} \ln(\sin(2x)) \, dx \), we can use a property of definite integrals.

### Step 1: Use the property of definite integrals
We know that:
\[ \int_{a}^{b} f(x) \, dx = \int_{a}^{b} f(a + b - x) \, dx \]
In our case, \( a = 0 \) and \( b = \frac{\pi}{2} \). Thus, we can write:
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