How do you get a regex from this DFA? I've been trying for hours. I'm teaching myself automata theory right now and I have this DFA:



And I'm trying to create a regex from it by removing q1 first and then q2. I already managed to remove q1 by doing it like this:



But now I'm not sure how to continue. The next step I'm trying to do is remove q2 and then read the regex from it. Even after trying to wrap my head around it for a long time I didn't really get it. Hopefully someone here can help me :)
By reading a 0, your DFA switches its state from right to left, 
By reading a 1, it switches state from up to down. 
So to reach your final state $q_3$ your DFA has to read an odd number of 1's and an even number of 0's.
Therefore your language is $L=\{w \in \{0,1\}^*|  |w|_1 mod  2 = 1, |w|_0 mod 2 = 0  \}$