Final answer:
The troubleshooting technique being used is substitution, where a new cable modem is sent to the customer to test if the current modem is causing the unstable Internet connection.
Step-by-step explanation:
The troubleshooting technique being used in this situation is substitution. Substitution involves replacing a component in a system with a known working one to isolate and identify the cause of the problem. In this case, the technician is sending a new cable modem to the customer to test if the current modem is the source of the unstable Internet connection.