The first three terms of a geometric progression are $\sin\theta$, $\cos\theta$ and $2 - \sin\theta$ respectively, where $\theta$ radians is an acute angle.
(a)[3]
Find the value of $\theta$ from the given information.
(b)[3]
Using this value of $\theta$, find the sum of the first $10$ terms of the progression. Write the answer in the form $\frac{b}{\sqrt{c} - 1}$, where $b$ and $c$ are integers to be found.
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