Immediately following Hippolytus's high-strung tirade about women comes this speech:
τάλανες ὦ κακοτυχεῖς
τίν᾽ ἢ νῦν τέχναν ἔχομεν ἢ λόγον
670 σφαλεῖσαι κάθαμμα λύειν λόγου;
ἐτύχομεν δίκας. ἰὼ γᾶ καὶ φῶς:
πᾷ ποτ᾽ ἐξαλύξω τύχας;
πῶς δὲ πῆμα κρύψω, φίλαι;
675 τίς ἂν θεῶν ἀρωγὸς ἢ τίς ἂν βροτῶν
πάρεδρος ἢ ξυνεργὸς ἀδίκων ἔργων
φανείη; τὸ γὰρ παρ᾽ ἡμῖν πάθος
πέραν δυσεκπέρατον ἔρχεται βίου.
(sung) How luckless, how ill-starred, is the fate of women!  What arts do we have, what speech, once we have faltered, that can undo the knot our words have created? I have received my just deserts! Ho, earth, ho, light of the sun! How shall I escape what has befallen, how hide the painful fact, my friends?  What god, what mortal shall appear to help me, sit at my side, and lend hand to my unjust deeds? For my present misfortune crosses now—unhappy the crossing—to the farther bourne of life. Unluckiest am I of women!
Note how the root τύχη is interwoven, appearing in this brief speech four times. The word is capable of symmetrically opposite senses. It can carry the force of Fate, the act of a god, as well as the caprice of chance, fortune, mere accident.
The semantic force given to the word might change depending on whom one believes is speaking. If it's Phaedra, the sense can be fraught with the sense of Necessity. Indeed, the audience knows her predicament stems from the act of a goddess. If it's the Nurse, then translating τύχη as luck, fortune, or chance seem more suitable. In a sense, the sense of the scene and of the world it takes place in depends on who we hear speaking. The choice of character divides along the faultline within the complex sense of τύχη.
Further, to wish to solve the knot through techne is not unlike the earlier thinking of the Nurse who said she'd find a way out of Phaedra's problem through the use of some ἐπῳδαὶ καὶ λόγοι θελκτήριοι, or φάρμακον -- some incantations or charms, some drug . . .
When the Nurse (or Phaedra) in the speech we are discussing expresses her hopeless hope:
What god, what mortal shall appear to help me, sit at my side, and lend hand to my unjust deeds?
It's difficult to envision the proud, strong Phaedra saying this. It's the speech of the subject class, of those who serve. Besides: what "deeds"?
If so, then the voice of Phaedra that we hear when she next enters reverts to the grander style of vehement authority:
Vile destroyer of your friends, see what you have done to me! May Zeus the father of my race destroy you root and branch with his thunderbolt!  Did I not warn you—did I not guess your purpose?—to say nothing of the matters now causing me disgrace? But you could not bear to do so: and so I shall no longer die with an honorable name. I must plan anew.
That the community of readers of this play could be so divided over this question of "who is speaking?" is a sign that the language of this play rests -- restlessly -- on a very fine edge.