# 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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