Solve:
`sin2theta+sin4theta=costheta+cos3theta`

Explanation

To solve the equation \( \sin 2\theta + \sin 4\theta = \cos \theta + \cos 3\theta \), we can use trigonometric identities to simplify and solve for \( \theta \).

### Step 1: Use the sum-to-product identities
We can use the identities for the sum of sines and cosines:
- \( \sin A + \sin B = 2 \sin\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2}\right) \)
- \( \cos A + \cos B = 2 \cos\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2}\right) \)

Applying these identities, we rewrite the left-hand side:
...