You may have access to a student license for ArcGIS. However, for a simple task such as this, it will be easier to download and install QGIS. QGIS is a free, open source GIS platform.
Once you install QGIS, add a vector layer, select 'directory' and type 'OpenFileGDB'. You will then be able to access all the layers in the geodatabase. Select the layers you want to add to the map.
Then use the coordinate tools to calculate the latitude and longitude.
If you're trying to convert the data into a lat long projection system, use the projection tool to project the data into WGS84 or other geographic coordinate system.
It's not clear if you just want to get the coordinates in lat long or if you are trying to reproject your data to a different projection. I think you are just chasing coordinates.
There is a lot of documentation available for calculating coordinates in QGIS on this site and elsewhere online. If you get stuck after installing QGIS, check out the QGIS documentation: http://www.qgis.org/en/docs/index.html