The first sheet is polarized at 0 degrees and the second sheet is polarized at 90. When both sheets are on the window is black. When you draw a certain tiled pattern on the two sheets though, I hypothesize that you can mostly block the sun from any angle and let most of the ambient light in.
The only way I know how to solve this problem is w/ evolutionary algorithms, which might be well suited. I think someone here might have some mathematical insight into this though, so I'm putting it out there.
-- update --
OK so we need four sheets of LCDs, with each of the window layers having 2 LCD sheets each. Any light that goes through either layer is filtered with some pattern of 0' or 90' pixels.
Any random pattern, as long as the two layers have inverted pixels, will block the sun completely. Ambient light is allowed in at 50% brightness. So there you go.