Number of values of the parameter α∈[0,2π]  for which  the quadratic function, (sin⁡α)x2+2cos⁡αx+12(cos⁡α+sin⁡α) is the square of a linear function is

Given expression is a perfect square if Disc = 0⇒4cos2⁡α−2(cos⁡α+sin⁡α)sin⁡α=0⇒4cos2⁡α−2sin2⁡α−2sin⁡αcos⁡α=0⇒tan2⁡α+tan⁡α−2=0⇒(tan⁡α−1)(tan⁡α+2)=0⇒α=π4 or π−tan−1⁡(2)