## 4 Discussion
This relationship is indirectly related to the root torque, a critical factor in achieving desired orthodontic outcomes. Our findings suggest that alterations in torque are likely due to the interplay between the bracket base and the crown surface. We have demonstrated through our study that introducing specific angles, referred to as \(\alpha\)3 or \(\alpha\)5, during the bracket positioning process can lead to additional palatal or vestibular root torque in the lateral incisors. These findings are significant as they highlight the nuanced effects that bracket positioning can have on tooth movement. The torque discrepancy observed in our study may have a substantial impact on treatment outcomes, especially in terms of the final positioning of the lateral incisor. This aspect is critical as the lateral incisor position can influence the overall aesthetic and functional results of orthodontic treatment. However, it is imperative to consider that addressing torque issues in orthodontic treatment is a multifaceted challenge. While our study emphasizes the importance of the morphology of the labial surface of the tooth as a significant factor [7, 8], it is just one piece of a larger puzzle. The interaction between the archive and the bracket slot, as well as the precision during bracket positioning, are equally important factors that must be considered [7, 19, 20, 21, 22]. These elements collectively contribute to the expression of torque and, by extension, the overall effectiveness of the orthodontic treatment. The precision of bracket placement, the compatibility of the archive with the bracket slot, and the individual variations in tooth morphology all converge to determine the final orthodontic outcome. Therefore, a comprehensive understanding and consideration of these factors are essential for orthodontists in planning and executing effective treatment strategies. The dynamic interaction between the archive and the bracket slot, commonly referred to as torque play, has been meticulously examined by [PERSON] and [PERSON] [22]. Their findings underscore its significant impact on treatment outcomes, revealing that the angular effect of this interaction can be as substantial as \(36.1^{\circ}\). Consequently, it appears imperative for orthodontic practitioners to mitigate the influence of torque play to ensure consistent treatment results. To achieve this, the use of full-size archives in conjunction with stainless steel ligatures is recommended during the final stages of treatment. This approach is suggested as it potentially offers a more precise control of tooth position, thereby aligning more closely with the intended treatment plan and reducing variability introduced by torque play. In our study, we specifically focused on the area 3 to 5 mm from the incisal edge for bonding brackets on the incisors, following the standard practice referenced in the orthodontic literature [23]. Furthermore, we determined that a 2 mm scope was appropriate for our analysis. This decision was based on the observation that the majority of bracket base heights, measured from the gingival edge to the incisal edge of a bracket, typically slightly exceed 2 mm. Our study highlights the inherent challenges in achieving the ideal position of a directly bonded bracket. Often, the process of bracket placement inadvertently introduces \(\alpha\)3 or \(\alpha\)5 angles, which can have significant implications for the treatment's effectiveness. This complexity is further emphasized by the findings of [PERSON] et al. [21], who demonstrated that even when brackets are placed by experienced orthodontists, there is an average vertical position variation of 0.34 mm, with a considerable standard deviation of 1.80 mm. This variability, although seemingly small, can have profound effects on the final orthodontic outcome, particularly in terms of root torque.