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Question 168

Let $$\alpha, \beta$$ be such that $$\pi < \alpha - \beta < 3\pi$$. If $$\sin\alpha + \sin\beta = -\frac{21}{65}$$ and $$\cos\alpha + \cos\beta = -\frac{27}{65}$$, then the value of $$\cos\frac{\alpha - \beta}{2}$$ is

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