Identify Fake Instagram Email

I have the username of a fake Instagram profile that has been harassing me and I need to discover the Gmail (or any registered email) sitting behind it so I can put a stop to the harassment before it escalates. No other steps have been taken so far—no reports, no cross-checks, nothing—so you will be starting with a clean slate and only that single piece of data.

Your task is to apply any legitimate OSINT techniques, metadata analysis, data-breach look-ups, or other investigative methods you are comfortable with to trace the username back to its underlying email address. The end result I’m looking for is either:

• The exact Gmail address (or confirmation that a different provider is used)
• A concise explanation of the evidence chain that connects the Instagram handle to that address

I will use the information solely to prevent further harassment; I do not intend to doxx or retaliate. Please outline upfront how long you expect the search to take and which public or proprietary tools you plan to lean on (Instagram Graph API, Hunter.io, Have I Been Pwned, Maltego, etc.) so I can be sure the approach remains ethical and within legal boundaries.