Change of Measure Using Levy Characterization

I have a standard brownian motion under probability measure $P$, let $Z(t)$ be the exponential martingale $Z(t)=exp{-thetaB(t)-1/2(theta)^2t}$. Define measure $Q(A)=E[Z(t)1a]$ as a probability measure. I need to show that the process $Xt=Bt+theta*t$ (Brownian motion with drift) is a standard brownian motion under measure $Q$ WITHOUT using C-M or Girsanov theorems, but instead using Levy's characterisation of brownian motion to show that under $Q$, $Xt$ is a cont. martingale.

I am pulling my hear out on this one!!