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Let $$\B_3$$ be the Artin braid group on $$3$$ strands and $$\PB_3$$ be the corresponding pure braid group. In this paper, we construct the groupoid $$\GTSh$$ of $$\GT$$-shadows for a (possibly more tractable) version $$\GTh_0$$ of the Grothendieck-Teichmueller group $$\GTh$$ introduced in paper \cite{HS-fund-groups} by D. Harbater and L. Schneps. We call this group the gentle version of $$\GTh$$ and denote it by $$\GTh_{gen}$$. The objects of $$\GTSh$$ are finite index normal subgroups $$\N$$ of $$\B_3$$ satisfying the condition $$\N \le \PB_3$$. Morphisms of $$\GTSh$$ are called $$\GT$$-shadows and they may be thought of as approximations to elements of $$\GTh_{gen}$$. We show how $$\GT$$-shadows can be obtained from elements of $$\GTh_{gen}$$ and prove that $$\GTh_{gen}$$ is isomorphic to the limit of a certain functor defined in terms of the groupoid $$\GTSh$$. Using this result, we get a criterion for identifying genuine $$\GT$$-shadows.