Trigonometry! #103

Geometry Level 5

The sides of a triangle inscribed in a given circle subtend angles α\alpha, β\beta and γ\gamma at the centre. Then find the minimum value of the arithmetic mean of cos(α+π2)\cos\left(\alpha+\frac{\pi}{2}\right), cos(β+π2)\cos\left(\beta+\frac{\pi}{2}\right) and cos(γ+π2)\cos\left(\gamma+\frac{\pi}{2}\right).

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

This problem is part of the set Trigonometry.

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