Question about Perfect Middle ending formations

Hello, I’ve been learning the Perfect Middle and had a question regarding the verb θάπτω. I noticed the 3rd person plural is τεθάπαται. I can’t seem to find an explanation as to why this formation occurs–my textbook only discusses the changes consonants undergo which yield another consonant and I don’t understand why the alpha appears in the ending here.

Can someone please help me understand what I’m missing?

THANKS

Smyth might give the answer (Greek grammar : Smyth, Herbert Weir, 1857-1937 : Free Download, Borrow, and Streaming : Internet Archive)

§465 f:

Stem ending in a Consonant + νται > Stem Ending in Consonant + αται.

If you want to know more about this, you could have a look at these grammars (in German!)

Schwyzer, I 671 § 3

Kühner-Blass. II 74ff.

Or you could read Sophocles’ Oedipus Rex, where the messenger recounts Oedipus’ self-blinding after Jocasta’s suicide:
ὁ δ᾽ ὡς ὁρᾷ νιν, δεινὰ βρυχηθεὶς τάλας
χαλᾷ κρεμαστὴν ἀρτάνην. ἐπεὶ δὲ γῇ
ἔκειτο τλήμων, δεινὰ δ᾽ ἦν τἀνθένδ᾽ ὁρᾶν.
ἀποσπάσας γὰρ εἱμάτων χρυσηλάτους
περόνας ἀπ᾽ αὐτῆς, αἷσιν ἐξεστέλλετο,
ἄρας ἔπαισεν ἄρθρα τῶν αὑτοῦ κύκλων,
αὐδῶν τοιαῦθ᾽, ὁθούνεκ᾽ οὐκ ὄψοιντό νιν
οὔθ᾽ οἷ᾽ ἔπασχεν οὔθ᾽ ὁποῖ᾽ ἔδρα κακά,
ἀλλ᾽ ἐν σκότῳ τὸ λοιπὸν οὓς μὲν οὐκ ἔδει
ὀψοίαθ᾽, οὓς δ᾽ ἔχρῃζεν οὐ γνωσοίατο. (1265-1274)

Here we have three future optatives in reported speech. The two -ατο endings in 1274, ὀψοίατο (elided) and γνωσοίατο, are grammatical equivalents of the -ντο ending of ὄψοιντο in 1271, differing both metrically and stylistically.