Why the movie title Tears of the Sun(2003)?
From the interview with director Antonie Fuqua
Tears of the Sun is the tears of the people of Africa. I think that once you see the movie, you get a sense of it. I don’t think you can make it clear to the audience because of the nature of the film. The trailers and all that stuff gears it more toward the action. You don’t really see the suffering so it’s difficult.
This movie tells the worse situation of people of Africa.
I think the movie title refers to the fact that in a land where the sun shines on everyone equally its people are being killed and therefore the sun is crying. The word "sun" here is also a play on words. In Africa people often use the term being a child or "Son" of Africa. Hence Tears of the Sun could also be read as "Tears of the Son", where the children of Africa are crying.
As a side note the film was actually filmed in Hawaii.