Kepler's Second Law of Planetary Motion. Solving for Theta at a known time in orbit.  how can I use Kepler's second law to solve for the value of (THETA).Thank you. P.S. I am also interested in the values of r and r's corresponding height at time t as stated in the law's description.

The area of the ellipse is $\pi a b$, so given that you know the period you know $\frac {dA}{dt}= \frac {\pi a b}{\text{1 year}}$ Then $\frac {d\theta}{dt}=\frac 2{r^2}\frac {dA}{dt}=\frac {2 \pi a b}{r^2\text{1 year}}$ Now use the orbit equation to replace $r$ with a function of $\theta$ and you have an equation you can integrate, at least numerically.