In chapter 11 page 15 example 11.2 and the next question on page 16 q 11.7 how do I get my first estimate for (thita1) for trial and error purpose?
That purely depends on your instinct ...as theta can take values only between 0 and 1 so, it wont be that difficult I guess to estimate the value. What I do is that I try to take 0.5 first ,then all depends on how close or far my ans is from the required, adjust the theta value to get an interval in which the answer required lies, followed by interpolation. They may be other several methods also.