{sqrt(.5), 0, 0, sqrt(.5)} * {{Cos[pi/8], Sin[pi/8], 0, 0}, {Sin[pi/8], -Cos[pi/8], 0, 0}, {0, 0, Cos[pi/8], Sin[pi/8]}, {0, 0, Sin[pi/8], -Cos[pi/8]}}

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