Better to start again than search for mistake! You are going in circles or backwards in what is a two-line argument. By #8 or again in #18 you had the expression for θ - which is nothing but rewriting the definition of 1b in chemical/mathematical terms. Why go looking for 1/θ or θ/(1-θ) when you are asked for θ? On RHS of the said equation for θ you have one thing twice and another one once. In #1 you have a relation between those two things. Start again and use that relation to eliminate one of them!