Definition: Zetetic as an adjective means "proceeding by inquiry"; as a noun, it means "skeptic".
Pronunciation: Zeh, teh, tick
Origin: Zetetic comes from Greek zeeteetikos (ζητητικός ) meaning "seeking".
Why use it? The adjectival sense of zetetic is a one word synonym for a three word phrase. One can use it to contrast, say, dogmatic religions and other things: "Fundamentalism usually is accepted on faith, but science and philosophy are both zetetic".
Examples: I read this word in Modernity and its Discontents