A geometry problem by Bala vidyadharan

Geometry Level 3

\[\begin{cases} a= \cos\alpha +\cos\beta \\ b = \sin\alpha +\sin\beta \\ 2\theta = \alpha -\beta \\ \end{cases} \]

If \(\alpha , \beta, a,b\) and \(\theta\) satisfy the system of equations above, state the value of \( \dfrac{\cos(3\theta)}{\cos(\theta)} \) in terms of \(a\) and \(b\).

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