II$.$ Consider the function $f$ with $f(x)=x(-x)$ for $f\frac{8}{}{\displaystyle \underset{n=1}{\overset{}{}}}\frac{sin(2n-1)x}{(2n-1{)}^3}1-\frac{1}{3^3}+\frac{1}{5^3}-\frac{1}{7^3}+\frac{1}{9^3}-\frac{1}{{11}^3}+$dots$0.$

$a.$ Prove that the Fourier $sine$ series $offis\frac{8}{}{\displaystyle \underset{n=1}{\overset{}{}}}\frac{sin(2n-1)x}{(2n-1{)}^3}$

$b.$ Deduce the sum $of$ the series $1-\frac{1}{3^3}+\frac{1}{5^3}-\frac{1}{7^3}+\frac{1}{9^3}-\frac{1}{{11}^3}+$dots