Access the Internet and go to the Trapcall website referenced below.
Choose one of their payment plans depending on what other service you may need and sign up. As of 2010, the fees start at around $5.
Use the unblock private number plan through your Trapcall plan by pressing the ignore or reject button on your phone as soon as the private caller calls you. Contact the Trapcall people to ask them how to do this with your particular phone.
Wait. Trapcall is doing its job of finding out the number and possible identification of this private caller and will call you back with that information. See how this works by watching the video on the website.
Listen and watch for the private caller to call again with the number unblocked.