New MacBook Pro 13” screen goes black when opened past vertical

This is a common issue with MacBook Pro 13" devices that are older, the issue is that the LVDS cable or backlight power cable have begun to fail.

This isn't a software issue and will require a hardware repair. You've not specified how old the machine is, you can do the following to find out:

1. Click the Apple logo in the menu bar.

2. Click About this Mac.

3. Look here:

You could additionally verify this is a hardware fault by connecting an external screen, or projector via the Mini DisplayPort/Thunderbolt or HDMI ports and verify this issue doesn't happen on the external monitor at the same time as the internal one.