Help me calculate integral $J=\int_{C} y^{2}z^{2}dx + x^{2}z^{2}dy + x^{2}y^{2}dz$ using Stokes theorem

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Task: Calculate integral using stokes theorem.

I'm getting stack in calculating the integral $$J=\int_{C} y^{2}z^{2}dx + x^{2}z^{2}dy + x^{2}y^{2}dz$$ where $$C: \begin{cases} x&=a\cos(t)\\ y&=a\cos(2t)\\ z&=a\cos(3t). \end{cases} $$ and $a=const$ we should integrate increasing t. The answer is 0. Please, give me some hints, because I'm new to this kind of integrals and it's quite difficult for me to understand it. Or if you can solve it with explanation. Thanks everyone.