Can we solve $\cos\theta - \sin (2\theta) + \cos (3\theta) - \sin (4\theta) = 0$?

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Give the general solutions of the following equations

1. \(2\sin 3\theta - 7 \cos 2\theta + \sin \theta + 1 = 0\),

How might we reduce the number of different multiples of \(\theta\)?

Can we turn the LHS into a function of \(\sin \theta\) alone, or of \(\cos \theta\) alone?

2. \(\cos\theta - \sin 2\theta + \cos 3\theta - \sin 4\theta = 0\).

How can we simplify an expression like \(\cos A + \cos B\)? Are there any identities that could help us?