First, we need to find the Fourier sine coefficients, which are given by the formula:
$$b_n = \frac{2}{L} \int_0^L f(x) \sin\left(\frac{n\pi x}{L}\right) dx$$
In our case, the function is $f(x) = 3x^2$ and the interval is $0 < x < 1$, so $L = 1$.
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