How am I supposed to prove the same using natural deduction? I started my proof with a LEM $$\Box (\Box p \rightarrow \Box q) \vee \neg \Box (\Box p \rightarrow \Box q)$$ I split the LEM via $\vee$ elimination, take the part before the $\vee$, and then add $\Box (\Box q \rightarrow p)$ by $\vee$ introduction.
Now for the part after the $\vee$ in the LEM. How am I supposed to use it to reach my conclusion? I tried by assuming $\neg \Box \Box (q \rightarrow p)$, my intention being that I would able to prove it wrong and thereby proving $\Box \Box (q \rightarrow p)$ being true, and thereafter is trivial.
Any help on this problem is highly appreciated.