Finding angle of a reflected isosceles triangle

[Brown Arrow]

Homework Statement

I am trying to find the following (marked in red) angle, I know that the radii to the points of contact make an angle θ with the horizontal.

Homework Equations

all angles of a triangle add up to 180 degrees.
isosceles triangle, has two equivalent sides

The Attempt at a Solution

I tried using symmetry and found the part in red is $\pi$ - 2$\theta$
but according to the text, the angle is 2$\theta$. I am confused on why is is 2$\theta$

 

[Simon Bridge]

The sides of the inverted triangle are tangents to each circle.
The base of your blue triangle is 2R.
The angles on either side of the base must be $\theta$.

The blue-triangle apex angle must be $\pi-2\theta$ ... which is where you've got up to.

The apex of the blue triangle forms a diamond shape with the inverted triangle.
The bottom of the diamond is the angle you want.
The left-hand angle is the same as the right-hand angle - you actually know what these angles are!

What do the angles in the diamond add up to?
What do the left hand and right hand angles add up to?