Find all squares, if they exist, on an 8 x 8 checkerboard

Chapter 1, Problem 1.7.46

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Find all squares, if they exist, on an 8 x 8 checkerboard so that the board obtained by removing one of these square can be tiled using straight triominoes. [Hint: First use arguments based on coloring and rotations to eliminate as many squares as possible from consideration.]

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