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For a connected graph \( G \) of order at least \( 3 \) and an integer \( k \geq 2 \), a \emph{twin edge} \( k \)-coloring of \( G \) is a proper edge coloring of \( G \) with the elements of \( \mathbb{Z}_k \), so that the induced vertex coloring in which the color of a vertex \( v \) in \( G \) is the sum (in \( \mathbb{Z}_k \)) of the colors of the edges incident with \( v \) is a proper vertex coloring. The minimum \( k \) for which \( G \) has a twin edge \( k \)-coloring is called the \emph{twin chromatic index} of \( G \) and is denoted by \( \chi_t'(G) \). It was conjectured that \( \Delta(T) \leq \chi_t'(T) \leq 2 + \Delta(T) \) for every tree of order at least \( 3 \), where \( \Delta(T) \) is the maximum degree of \( T \). This conjecture is verified for several classes of trees, namely brooms, double stars, and regular trees.