The engine calls <modc_predict> when reprediction is required. This happens usually when new data has arrived from the server. <modc_predict> should to prediction from the current snapshot and current snapshot tick (<client_tick> + 1) up to and including the tick returned by <client_predtick>.
Predicted input sent to the server can be retrived by calling <client_get_input> with the corresponding tick that you want the input for. Here is a simple example of how it might look.