Trigonometry! #7

Geometry Level 4

Let α,β\alpha, \beta be such that π<αβ<3π\pi < \alpha - \beta < 3 \pi .

If sinα+sinβ=2165\sin \alpha + \sin \beta = -\frac {21}{65} and cosα+cosβ=2765\cos \alpha + \cos \beta = -\frac {27}{65}, then cos(αβ2)\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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