Find an upper and lower bound for the reciprocal of the modulus of $\displaystyle z^4-5z^2+6$ if $\displaystyle |z|=2$

$\displaystyle n\leq\frac{1}{|z^4-5z^2+6|}\leq m$

Out of all the the ways to break modulus how do I know which structure of the triangle inequalities to use?

$\displaystyle |z^4-5z^2+6|=|(z^2-3)(z^2-2)|\geq|z^2-3||z^2-2|=||z|^2-|3||*||z^2|-|2||$$\displaystyle =|4-3||4-2|=1*2=2$

$\displaystyle |z^4-5z^2+6|\leq|z|^4-5|z|^2+6=2^4-5*2^2+6=16-20+6=2$

Why am I getting the same value for my upper and lower bounds?