For any real number $x,$ let $$\left[ x \right]$$ denote the largest integer less than or equal to $x.$ Let $f$ be a real valued function defined on the interval $$\left[ { - 10,10} \right]$$ by $f\left( x \right) = \left\{ {\begin{matrix} {x - \left[ x \right]} & {if\left[ x \right]is\,odd,} \\ {1 + \left[ x \right] - x} & {if\left[ x \right]is\,even} \\ \end{matrix} } \right.$ Then the value of $${{{\pi ^2}} \over {10}}\int\limits_{ - 10}^{10} {f\left( x \right)\cos \,\pi x\,dx}$$ is