Three $\theta$ s

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 $\text{\_\_\_\_\_\_\_\_\_\_}$ .