Am I going in the right direction?

Because Z = 2*sintand Z = 1 then t = pi/6 or 5pi/6

now X and Y both equal (5-sqrt(3))/sqrt(2) so going back toX(s,t) I can see that sinsand cossneed to equal each other. This happens at pi/4 or 5pi/4

Sosandtare pi/4 and 5pi/6

Am I headed in the right direction???????????????????