Let X1,.., Xn ∼ U(0, θ). Show that the MLE is consistent.

Hint: Let Y=max {X1,... ,Xn}, for any c, P(Y <c)=P(X1 <c,X2 <c,...,Xn <c)=P(X1 <c)P(X2 < c)...P(Xn < c).

So I know for the MLE to be consistent, the estimated value of theta has to converge (in probability) to the actual value.

Im trying to think of how this hint given can lead me to the result.