TMUA 2019 · Paper 1 · Question 14

$x$ satisfies the simultaneous equations

sin 2 x + 3 cos 2 x = - 1

and

3 sin 2 x - cos 2 x = 3

where $0^{\circ} \leq x \leq 36 0^{\circ}$ .

Find the sum of the possible values of $x$ .