Here's my blocked-out setup with modifier setup. The base tile was created from a circle (here with 8 vertices) from which later on 7 parts were deleted. Array rotation in Z is 45° (360°/8). For better modeling it makes sense to set your outer edge of the tile parallel to the Y or X axis (rotate tube&empty around curser at center)
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Another improvement, if your tile is mirrored, would be to add a further mirror modifier around Y or X as the first modifier:
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