\(ABCD\) is a square lying symmetrically inside a sector of a circle whose radius is \(\quantity{1}{in.}\), the angle of the sector being \(60^\circ\). \(A\) and \(B\) lie on the straight boundaries, \(C\) and \(D\) on the curved boundary. Calculate:

- the length of the arc \(CD\),
- the area \(ABCD\),
- the area of the minor segment of the circle cut off by the chord \(CD\).

[Answers to (i) and (iii) may be left in terms of \(\pi\).]