algorithms – 𝑇(𝑛) = 4𝑇(𝑛/2) + 𝑛^2 / log 𝑛 , 𝑇(1) = 0 solve and later proof by induction

I spent 3 days on trying to solve this question.
Someone please solve and proof it by induction.
It is the first time I am dealing with a recursion relation that involves logs.

Please solve and proof it for me so that I can understand what I’ve been doing wrong.

It needs to be solved through iterative substitution method.

Edit:

So final answer is n^2loglog(n);
but then how do you Proof it by induction…

how will you prove the original equation confirms to P(k+1), i.e.

(k+1)^2loglog(k+1)