I did the FBD, and I found too many variables which are not eliminating...Moreover, I believe this question is based on kinetic and static friction. But, $\mu$ here is ambiguously defined...How Do I get the integral value?
For pushing it up, we have to overcome friction(act downwards) as well as the $mg\sin\theta$. So, $$3N=f+mg\sin\theta$$
Now the block is just slipping , so friction is acting upwards, and so does the force applied externally.So, $$N+f=mg\sin\theta$$
Eliminate $N$ and use $f=\mu mg\cos\theta$.
Solve for $\mu$ you get your answer.