<image>As shown in Figure ①, there is a rectangle with a length of 2m and a width of 2n, which is evenly divided into four smaller rectangles along the dashed lines in the figure, and then assembled into a square as shown in Figure ②.

(1) The side length of the large square in Figure ② is ____; the side length of the shaded square is ____;
(2) Express the area of the shaded part in Figure ② in two different ways;
(3) Observe Figure ②, what is the quantitative relationship between the three algebraic expressions (m+n)², (m-n)², and mn? If |m+n-6| + |mn-4| = 0, find the value of (m-n)².