The limit

\[ \lim_{x \to 3} \left [ \frac{1}{(9-x^2)^{2}} \left( \frac{9+x^2}{3x} - 2\sin \frac{3π}{2} \sin \frac{πx}{2} \right) \right ] \]

can be expressed as \( \displaystyle \frac{a + b \pi^ c}{d^a} \) for positive integers \(a,b,c\) and \(d.\)

What is the value of \(a+b+c+d?\)

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