Two Functions Having Something Common

Algebra Level 4

Given that \(f(x)=\sin x\) and \(g(x)=x/10\). If \(x_{1},x_{2},...,x_{n}\) are the values of \(x\) for which \(f(x)=g(x)\), then find the maximum possible value of \[\dfrac {\left\lfloor x_{1}\right\rfloor- \left\lfloor x_{2}\right\rfloor+\left\lfloor x_{3}\right\rfloor-\left\lfloor x_{4}\right\rfloor+\cdots\pm \left\lfloor x_{n}\right\rfloor-1}{n-1}.\]

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