Trigonometry! #7

Geometry Level 4

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 \(\cos (\frac {\alpha - \beta}{2})\) is

The calculations are pretty complex, so I advise you to go open a calculator.

This problem is part of the set Trigonometry.

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