Recurrence : $T(n) = 4T(n/2) + Θ(n^2/\log n)$ Is there a way to solve this recurrence using master theorem:

$$T(n) = 4T(n/2) + Θ(n^2/\log n)$$
As mentioned by @Yuval Filmus in the comment, you can use the extension of the master theorem (case 2b). The result is $T(n) = \Theta(n^2 \log\log{n})$.