Why was "ein" used here after a masculine plural noun?

Question

Er setzt sich falsche Zähne ein, [...]. -- Source

If I am not wrong, Zähne is a masculine plural and hence I think the ein here is gilding the lily.

Answer 1

That ein at the end of the sentence corresponds to the ein contained in the separable verb einsetzen. There is no relation to articles whatsoever. Moreover, unlike other languages (Polish, French, Spanish, etc.), in German there is no masculine plural, every noun is collapsed, grammatically seen, to just plural.

Answer 2

Here, ein is not the indefinite article, nor does it refer to the number one. Instead, it belongs to the separable verb einsetzen, a short form of hineinsetzen, and it means to put something in or into something else.

Answer 3

Ein has other responsibility in addition to what you know. In German language, there are separable and inseparable verb prefixes. (There is a good handout to learn these prefixes).

As you also see in the tutorial, ein is a separable verb prefix. The verb in your example is einsetzen.

The other examples with ein could be;

einschlafen - Ganz allein schlafe ich nicht ein

einkaufen - Ich kaufe nicht mehr ein