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If \(\cot \theta + \tan \theta = x\) and \(\sec \theta - \cos \theta = y\), then prove that \((x^2 y)^{\frac{2}{3}} - (x y^2)^{\frac{2}{3}} = 1\).
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This is a self-assessment task. Solve this question and assess the solution steps after completing the test on your own.