Absolutely continuous with respect to Wiener measure

Question

Consider the Wiener measure $\mu$ on $\Omega:=\{x:[0,1]\to\mathbb{R}:x\in\mathcal{C}([0,1]),x(0)=0\}$ and define for $\theta\in\mathbb{R}$, \begin{align} \frac{d\mu_\theta}{d\mu}(x)=e^{\theta x(1)-\theta^2/2}. \end{align} How do I compute the distribution of the coordinate process under $\mu_\theta$, i.e. $\mu_\theta(X_{t_0}^{-1}(A_0)\cap\cdots\cap X^{-1}_{t_n}(A_n))$ for $A_0,\dots,A_n\subset\mathbb{R}$ Borel and $X_t:\Omega\to\mathbb{R}$ defined by $X_t(x)=x(t)$?