1. Anytime you reduce a JPG, you get loss of quality.
2. If you simply resize it so that the largest dimension is 75 pixels, then it really shrinks the smaller dimension.
What I've done is two versions. The first is just resizing the largest dimension to 75 pixels. The second is where I cropped the crowd on the left and right, and then resized it to 75. While not exactly 75 x 75, it's pretty close (it's 75 pixels in width, 69 pixels in height). I'd bet some of the graphics gurus can do a better job, though...