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I want to find the coefficient of $[a^3b^3c^3]$ in the expansion of $$\bigg[1-\bigg(\frac{a+a^2}{1-(a+a^2)}+\frac{b+b^2}{1-(b+b^2)}+\frac{c+c^2}{1-(c+c^2)}\bigg)\bigg]^{(-1)}$$

I have made research on internet about coefficient of this multivariable generating function, but could not find something valuable. Can you help me to calculate the coefficent using Sagemath ?