Installing flatscreen in front of front window?

[JohnUSA]

In the closed position, does anyone know how much space is available in the front curved area, right under the window valance? Seems like a good spot to put a flat screen.
Thinking about a swing-away mount right next to the window, to allow the tv to fold up against the window while the top is stowed, and then swing over to a corner when the top is raised. Seems like a natural void space.