Thanks for removing the solution, that way I got to try it. My method is in white. I gave up on that 8 queens puzzle so I way happy to be able to do this one.
I placed the 3 black queens first, and then checked if 5 squares were not attacked. I tried to minimize ranks and files and maximize overlap of attacked squares. Finding a few that allowed 4, I finally settled with two in the top left corner touching orthogonally and then counted the overlap of the third. If I could free up one square (increase overlap by 1) then it's solved. Which happened. Took me ~15 minutes. Pretty quick after I thought of that method.
There are no other solutions except the seven other symmetrical ones.