MathNet 2014 Question 28

Let $[x]$ denote the greatest integer not exceeding $x$. Find the last two digits of $\lfloor \frac{1}{3} \rfloor + \lfloor \frac{2}{3} \rfloor + \lfloor \frac{2^2}{3} \rfloor + \dots + \lfloor \frac{2^{2014}}{3} \rfloor$.