# Trigonometry! #103

Geometry Level 4

The sides of a triangle inscribed in a given circle subtend angles $$\alpha$$, $$\beta$$ and $$\gamma$$ at the centre. Then find the minimum value of the arithmetic mean of $$\cos\left(\alpha+\frac{\pi}{2}\right)$$, $$\cos\left(\beta+\frac{\pi}{2}\right)$$ and $$\cos\left(\gamma+\frac{\pi}{2}\right)$$.

If the minimum value can be expressed as $$- \sqrt{ \frac{a}{b} }$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a + b$$?

This problem is part of the set Trigonometry.

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