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$\sin (A) \sin(2A) \sin(3A) \sin(4A) = ax^2 + bx^3 + cx^4 + dx^5$

If $\sin^{2}(A)= x$ and that the equation above is satisfied for constants $a,b,c,d$, then find the value of $12a - 10b +8c -11d$.

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