An astronomer notes a telescope pointing direction of 1234.56789∘.
(i) Find the equivalent positive angle between 0∘ and 360∘, correct to four decimal places.
(ii) Express 1234.56789∘ in the form D∘M′S′′, rounding the seconds to the nearest second.
(iii) Convert the equivalent angle obtained in part (i) to D∘M′S′′, again rounding to the nearest second.
(iv) Compare the answers of parts (ii) and (iii) and explain briefly why the degree component of part (ii) differs from that of part (iii).