It's less of a problem that police lie if everyone adopts the very clear advice given by every legal professional:
> Never, ever, talk to police.*
* You can give them your name, and if they ask "what are you doing", a tolerable answer, but any further questions are to be met with "I have been advised to never speak with police, and I can answer no further questions."
Here's an entertaining lecture on the topic, for anyone not convinced: https://www.youtube.com/watch?v=d-7o9xYp7eE&t=11s
And he wrote a very short (single-sitting) book titled: "You Have The Right To Remain Innocent": https://www.amazon.com/You-Have-Right-Remain-Innocent-ebook/...
Do. Not. Talk. To. Police. They are not your friend.
If you're reading this and about to hit the "reply" button explaining why I am wrong, will you please, please say in that comment if you watched _any_ of the lecture by Regent Law Professor James Duane?