Determine all the possible values where 0 degree <= x <= 360 degree such that;
sin x sec x - 3 sin x = 0
First of all, your third line is incorrect, since when you multiply everything through by $\displaystyle \cos{(x)}$ you're supposed to get $\displaystyle \displaystyle \sin{(x)} - 3\sin{(x)}\cos{(x)} \ 0$.
Anyway, you should factorise the entire expression first and set each factor equal to 0.
$\displaystyle \displaystyle \begin{align*} \sin{(x)}\sec{(x)} - 3\sin{(x)} &= 0 \\ \sin{(x)} \left[ \sec{(x)} - 3 \right] &= 0 \\ \sin{(x)} = 0 \textrm{ or } \sec{(x)} - 3 &= 0 \end{align*}$
Go from here...