If S ={ a ∈ R:|2 a -1|=3[ a ]+2{ a }}, where [ t ] denotes the greatest integer less than or equal to t and { t } represents the fractional part of…

If $\displaystyle \mathrm{S}=\{\mathrm{a} \in \mathrm{R}:|2 \mathrm{a}-1|=3[\mathrm{a}]+2\{\mathrm{a}\}\}$, where $\displaystyle [\mathrm{t}]$ denotes the greatest integer less than or equal to t and $\displaystyle \{\mathrm{t}\}$ represents the fractional part of t , then $\displaystyle 72 \sum_{\mathrm{a} \in \mathrm{S}} \mathrm{a}$ is equal to $\displaystyle \_\_\_\_$.