I see that this is impossible. The correct answer is currently basically impossible;) Using programming, you can create a transparent window or application. I have never done anything like this, but I used several programs that let me control transparency.
My best bet for controlling window opacity is DirectX. So, if you have to make a browser with DirectX, you can control the opacity of the window by reading CSS.
So you could do it yourself, just like mozilla firefox reads its own css (-moz-radius), just create your own DirectX based web browser. I could see someone getting a lot of support in a similar project.
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