$2.$ Draw the root locus for the unity feedback system shown in Fig. $2$ by answering all the questions below.

Fig. $2.$ A unity feedback system.

$($a$)$ Identify all the starting and ending points of the locus, including the infinity zeroes $($if applicable$).$

$(4$ marks$)$

$($b$)$ Find all the arrival angles.

$(2$ marks$)$

$($c$)$ Find all the break$-$in and break$-$out points $($if applicable$).$

$(2$ marks$)$

$($d$)$ Manually sketch the root locus.