This app was mentioned in 2 comments, with an average of 2.00 upvotes
Try this, which should work in several Italian cities: https://play.google.com/store/apps/details?id=it.ud.microtek.ITTaxi
There is also https://play.google.com/store/apps/details?id=taxi.android.client which has a tariff calculator. From the centre of Catania to Letojanni it says 82 € plus taxi call, so you would pay more than 160 €. While I'm sure you're going to catch a taxi fast in Catania, it could be more difficult in Letojanni when it's time to go back, so you maybe could ask the taxi driver to wait (of course this would cost you for his time).
At this point, maybe you could rent a car, and it would cost you much less.