You should never serve time for caving to polices bullshit tactics in an interrogation room. Their entire goal is to lie and manipulate you into giving the the exact answer they want, it's incredibly messed up.
I urge anyone to watch either The Confessions, a Frontline documentary about Norfolk Four, or The Central Park Five, a Burns documentary about a similar matter. You will never look at police interrogations the same way again.
Further, watch this shared lecture by a professor and a police integrator where they both vehemently state that you should never, ever talk to the police. Ever. Innocent or not. Ever.
https://www.youtube.com/watch?v=6wXkI4t7nuc