1. (cotè+1)(cscè-1/2)=0

2. sin²è-cos²è=1+cosè

I will replace è with Ø

1.
(cotØ+1)(cscØ-1/2) = 0

cotØ = -1 or cscØ = 1/2
tanØ = -1 or sinØ = 2 --->that is not possible

if tanØ = -1 then
Ø = 135° or Ø = 315°
Ø = 3π/4 or Ø = 7π/4

2.
sin^2 Ø - cos^2 Ø = 1 + cosØ
(1-cos^2 Ø) - cos^2 Ø - cosØ - 1 = 0
2cos^2 Ø + cosØ = 0
cosØ(2cosØ + 1) = 0
cosØ=0 or cosØ = -1/2
Ø = π/2 or Ø = 3π/2 or Ø = 2π/3 or Ø = 4π/3