Not sure if the original question serious thread of not.
No - you cannot project in sunlight - not morning, noon or even evening shade sunlight. You might be able to have some visible image in sunlight if you constructed a square frame all around your screen area that extends out far enough from the image - maybe four or five or six feet - that would block any direct sunlight hitting your image. I have seen stores attempt to demonstrate projection in the brightly lit showrooms this way - still doesn't work - viewers standing directly in front of this mess can see something but it ain't a good image - back to the answer - No.
TV displays don't work much in direct sunlight either - alternative answer is, yes, you will need a very, very expensive professional solution - like the jumbo-tron displays that work in daylight at football stadiums or the giant displays that run 24/7 in Times Square in New York City - can we say millions of $$$$$?
24/7 projection equals 168 hrs/week equals 672 hrs/month equals exhausted and probably dead lamp in 3 to 4 months equals bad idea.
No - 2.5 meter throw distance won't produce a 4 meter square image (with any projector I know of) - you will need an extremely bright professional display.
You don't share what your application is (that means, what in the world are you trying to accomplish?). It must be either some advertising gimmick or you want to drive a neighbor out of his or her mind.