If $p, q, r, s$ are in $A.P.$ and $f (x) =$ $\left| {\,\begin{array}{*{20}{c}}
{p\,\, + \,\,\sin \,x}&{q\,\, + \,\,\sin \,x}&{p\,\, - \,\,r\,\, + \,\,\sin \,x}\\
{q\,\, + \,\,\sin \,x}&{r\,\, + \,\,\sin \,x}&{ - \,1\,\, + \,\,\sin \,x}\\
{r\,\, + \,\,\sin \,x}&{s\,\, + \,\,\sin \,x}&{s\,\, - \,\,q\,\, + \,\,\sin \,x}
\end{array}\,} \right|$ such that $f (x)dx = - 4$ then the common difference of the $A.P.$ can be :
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