TH-TMO 2019 Problem 5

Let $a,b,c$ be positive reals such that $abc=1$ . Prove the inequality $$\frac{4a-1}{(2b+1)^2} + \frac{4b-1}{(2c+1)^2} + \frac{4c-1}{(2a+1)^2}\geqslant 1.$$