discrete mathematics - How to find the numbers of Bezout identity for two numbers

I'm having troubles finding two numbers a,b such that $288a+177b=3=gcd(177,288) (1)$

I've been writing the equations of the Euclids algorithm one over another many times to get any pair that verify (1). But, I don't get this yet. I'm trying to solve $288x + 177y = 69$ I understand very well the theorem. But I really, really need help finding the particular solution. If someone can explain me any method, or give me an advice to find a pair (a,b), I would really appreciate it. Thanks for reading,

Greetings!