# $\cot\theta + \tan \theta = x$ and $\sec \theta - \cos \theta = y$, evaluate $\left(x^2 y + xy^2\right)^{2/3}$

Given that $\cot\theta + \tan \theta = x$ and $\sec \theta - \cos \theta = y$, evaluate $\left(x^2 y + xy^2\right)^{2/3}$

I tried substituting $\cot \theta$ with $\frac{1}{\tan \theta}$ and similarly with $\sec \theta$, but it was of no help.

Please help me in simplifying this preferably with Pythagorean Identities. I found this question from the section of the book where it explains these identities, so I suppose we could use them here.

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$$\left(x^2 y + xy^2\right)^{2/3}=\left(xy(x + y)\right)^{2/3}$$ $$xy=\frac{\sin \theta}{\cos^2 \theta}$$ $$x+y=\frac{1+\sin^3 \theta}{\sin \theta\cos \theta}$$ $$xy(x+y)=\frac{1+\sin^3 \theta}{\cos^3 \theta}$$ $$\left(xy(x + y)\right)^{2/3}=\frac{(1+\sin^3 \theta)^{2/3}}{\cos^2 \theta}$$