solve the equation on the interval [0,360]

cos^2(t)+2cos(t)+1=0       factor

(cos (t) + 1)  (cos (t) + 1)  = 0

(cos (t) + 1 ) ^2  = 0         take the square root of both sides

cos (t)  + 1   =  0             subtract 1 from both sides

cos (t)  = -1           and this occurs at   t = 180°