R Gamliel seemingly wanted R' Yehoshua to come forward publicly with his shitah regarding Maariv (and in the ma'aseh with R Tzadok) so there could be a decision to clarify and establish the Halacha.
a] Why would R Yehoshua try to avoid coming forward with his shitah, if it will lead to the Chachamim being mevarer and koveah the Halacha?
b] How could R' Yehoshua say that he would have lied if no one could contradict him?
Dov , Ottawa, Canada
a) Tosfos (Bechoros 35b, DH v'Ki Teima) writes that it was out of honor for Raban Gamliel that Rebbi Yehoshua did not want to say what his Shitah was.
b) One of the Rishonim, in Teshuvos Rabeinu Avraham ben Yitzchak Av Beis Din (#27), writes that this was not considered a lie because one is permitted to change one's words for the sake of peace (see Yevamos 65b). Rebbi Yehoshua wished to prevent quarrels among the Jewish people.
Kol Tuv,
Dovid Bloom
(P.S. For a comprehensive and ingenious exposition of this incident and the perplexing parts of it, see Rav Yehonasan Eyebshitz in Ya'aros Devash #18.)