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Find the values of theta, for which cos3...

Find the values of `theta`, for which `cos3theta + sin3theta + (2sin2theta-3)(sintheta-costheta)` is always positive.

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To solve the problem, we need to find the values of \( \theta \) for which the expression \( \cos 3\theta + \sin 3\theta + (2\sin 2\theta - 3)(\sin \theta - \cos \theta) \) is always positive. ### Step-by-Step Solution: 1. **Rewrite the Expression**: We start with the expression: \[ \cos 3\theta + \sin 3\theta + (2\sin 2\theta - 3)(\sin \theta - \cos \theta) ...
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