“in-vay-gull” | /ɪnˈviː.ɡəl/
v – To convert, convince, or win over with flattery or wiles.
“The woman was able to inveigle her way into the private club by flirting with the security guard.”
Early corruption of French aveugler (“to blind, to delude”), from aveugle (“blind”), from the Old French avugle (“without eyes”), from Latin ab + oculus (“eye”). The in- might be from other a-/en- variations found in Middle English, which was then latinised into in-.