(a) Use the substitution \(u=1-(\theta-1)^{2}\) to find
\(\int \frac{\theta-1}{\sqrt{1-(\theta-1)^{2}}} \mathrm{~d} \theta .\)
(b) Find the solution of the differential equation
\(\theta \frac{\mathrm{d} y}{\mathrm{~d} \theta}-y=\theta^{2} \sin ^{-1}(\theta-1),\)
where \(0\lt \theta\lt 2\), given that \(y=1\) when \(\theta=1\). Give your answer in the form \(y=\mathrm{f}(\theta)\).