Evaluate: `int1/(sin^2x+sin2x)\ dx`

Explanation

To evaluate the integral \( \int \frac{1}{\sin^2 x + \sin 2x} \, dx \), we will follow these steps:

### Step 1: Rewrite the Integral
We start with the integral:
\[ \int \frac{1}{\sin^2 x + \sin 2x} \, dx \]
Using the double angle identity, we know that \( \sin 2x = 2 \sin x \cos x \). Thus, we can rewrite the integral as:
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