Known tip to RUB the screw with soap, to facilitate its mounting in the wooden piece. If it is plastic, for example, sealing the dowel into the hole — then the screw for the same purpose, it is expedient, in any way, and heated screw hot: it will opravit dowel and will hold tightly.
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If you make the fixture shown in the picture, then cropped the Wallpaper strip will have the same dimensions and strict perpendicularity of the cutting line.