Infinite Sequences and Series · Superchallenge problem

Let $S=\displaystyle\sum_{n=1}^{\infty}\frac{\cos(n\pi/4)}{3^n}$ and $T=\displaystyle\sum_{n=1}^{\infty}\frac{\sin(n\pi/4)}{3^n}$. Find the exact value of $S^2+T^2$.