Solve `sin 2x - sin 4x + sin 6x = 0`.

Explanation

To solve the equation \( \sin 2x - \sin 4x + \sin 6x = 0 \), we will follow these steps:

### Step 1: Use the sum-to-product identities
We can use the identity for the sum of sines:
\[ \sin A + \sin B = 2 \sin\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2}\right) \]
In our case, we can group \( \sin 6x \) and \( -\sin 4x \):
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