A Transformation that maps a probability distribution onto another

Question

I am trying to find if there exists a transformation (just a mapping) $T$ in closed form expressions that maps the probability distribution \begin{eqnarray*} f(x) = \begin{cases} \frac{2}{\theta}\left[1-\frac{x}{\theta}\right]& \text{for } 0\le x\le \theta \\ 0 & \text{for } x>\theta \end{cases} \end{eqnarray*} onto the probability distribution $$g(x) = \frac{1}{\theta}e^{-\frac{x}{\theta}}.$$ I tried if exponential mapping would work, but unsuccessful. Any help is greatly appreciated.