How do I get the dimensions (RECT) of all the screens in win32 API?

How do I get the dimensions (RECT) of all the screens in win32 API?

I'm writing an application for the testing team. What this application
does is it lets you take a screenshot of any part of the screen (and then
it uploads it to testing team server with comments).
Taking screenshot involves selecting the region on the screen to take
screenshot of. For this I'm creating a semi-transparent window and
overlaying it over the entire screen. I'm currently using
GetDesktopWindow() and GetWindowRect() to get the dimensions of the screen
but this doesn't work in multi-screen environments.
How do I overlay a window over all possible screens?
The screen configurations can be pretty exotic, such as:
[LCD]
[LCD][LCD][LCD]
(4 lcd screens - one at the top, 3 at the bottom)
Or
[LCD] [LCD]
[LCD][LCD][LCD]
[LCD] [LCD]
(7 lcd screens - 3 on the right, 3 on the left, 1 in the middle).
Etc.
Does anyone know how I could overlay 1 window all the screens? I wonder
what the dimensions would look like in the 1st exotic example, when there
is no screen on the top-row left and right?
Perhaps I should be creating one overlay window per LCD screen?
Any ideas?