Three \(\theta \)s

Geometry Level 5

Let \(ABC \) be an isosceles triangle with \(AB=AC\) and \(\angle A= 2 \theta \), \({ \theta }_{ 1 }\) is value of \(\theta \) for which inradius of \(\triangle ABC\) is maximum and \({ \theta }_{ 2 }\) and \({ \theta }_{ 3 }\) are solutions of \(\cos \theta = \theta \) and \(\sin \theta =\cos \theta \) is first quadrant respectively, then \(\text{__________} \).

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