Doctrine, dogma, tenet are synonymous only when they mean a principle (usually one of a series or of a body of principles) accepted as authoritative (as by members of a church, a school of philosophers, or a branch of science).
Doctrine is often used in a much broader sense to denote a formulated theory that is supported by evidence, backed by authority, and proposed for acceptance.
In the narrower sense doctrine retains its basic implication of authoritative teaching, but it presupposes acceptance by a body of believers or adherents.
Dogma also stresses authoritative teaching but unlike doctrine it seldom implies proposal for acceptance.
A dogma is not advanced as reasonable and worthy of acceptance but laid down as true and beyond dispute.
Dogma (or especially its derivative dogmatic) often connotes insistence, sometimes arrogant insistence, on authority or imposition by authority.
Tenet emphasizes acceptance and belief rather than teaching. It is therefore thought of as a principle held or adhered to and implies a body of adherents.