winapi - How do I create a capturable no-borders fullscreen window containing OpenGL content?

Question

I have a no-borders fullscreen window created with the WinApi function CreateWindowEx :

    m_window = CreateWindowEx(
        WS_EX_TOOLWINDOW | WS_EX_TOPMOST,
        winClassName,
        winName,
        WS_VISIBLE | WS_POPUP,
        CW_USEDEFAULT, CW_USEDEFAULT,
        GetSystemMetrics(SM_CXSCREEN), GetSystemMetrics(SM_CYSCREEN),
        NULL,
        NULL,
        hInstance,
        NULL
    );

If I try to take a screenshot of the window with the Print-Scr key, the window won't appear on the result (everything that is behind appears though).
Using WS_POPUP as window style seems to be the source of the problem, but I couldn't find any other way to create a no-border window with the WinApi.