A high-precision sensor measures the rate of energy dissipation, $R(t)$, in a prototype circuit over the interval $0\le t\le \frac{\pi }{6}$ seconds. The rate is modeled by the function:

$$R(t)=(3t-1)\cos (3t)$$

Given that the total energy dissipated, $E={\int }_0^{\frac{\pi }{6}}R(t)dt$, can be expressed in the form $a\pi +b$, find the exact value of $a$ and the exact value of $b$.

Fully justify your answer.