Big Theta Proof: May I chose any constant?
Yes, as long as the constant conforms to the definition of $\Theta$, that is it


is positive and
independent of $n$.


This follows directly from the definition of $\Theta$, which requires only the existence of some $c_1, c_2&gt;0$ (in typical formulations). 

You may find our reference questions helpful; in particular, there are more convenient ways to prove such claims besides checking the definition explicitly.