Coefficient of \(x^2\)

Let \(\color{orange}{C}\) be the coefficient of \(\color{green}{x^2}\) in \(\color{purple}{(1-x)(1+2x)(1-3x)(1+4x).........(1+14x)(1-15x)}\). Find \(\color{orange}{|C|}\).

[Credits to my math teacher.]

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