probability theory – Equivalence of two finite measures

My question is somehow similar to these equations in here, in here, and in here

let $mu_1$ and $mu_2$ be the two measures on $mathbb R$ such that
$mu_1((a,b))= mu_2((a,b)) < infty$ whenever $−infty < a < b <
for which $mu_{1}({ a})=0$, $mu_{1}({ b})=0$,
$mu_{2}({ a})=0$, and $mu_{2}({ b})=0$. Show that $mu_1(A) =
whenever $A in mathcal B$.​

I am not sure how would I use $pi$-system and $lambda$-systme in here. Any hints are appreciated.