I haven't installed string trees in many years. They were a 10¢ fix Leo implemented back 100 years ago to compensate for poorly cut nuts when his guitar designs went into production and the line workers couldn't (or didn't have time to) cut the nuts properly. Strings would pop out of the slots from lack of tension/retention. Prior to that, old acoustics tilted back the headstock for much the same reason, although beyond poorly cut nuts they were mostly strung with catgut or eventually nylon strings, which also had very low tension on them and suffered from spurious string displacement. Proper attention to nut fabrication precludes the need for trees.
Incidentally, the pic in your avatar is hosted sideways. Whoever your host or your pic display software is maybe rotating it to display proplerly on your monitor, but when it gets to the forum it doesn't know that, so it's displaying what it's being sent. You'll have to correct the original to get it to display properly here - there's no way for the forum software to adjust that. In order for me to fix it, I'd have to host it on another server where you wouldn't have access to it anymore, which wouldn't be desirable.