Trigonometry question?

Question

when solving for 0 < θ< or = 360
2tan( θ)= cos (θ)

so i want to see if my logic to solving is correct!
i found the angles are 90 and 270

Answer 1

The equation is 2tan( θ)= cos (θ)

Recall the trignometric quotient rule:tanθ=sinθ/cosθ

2sinθ/cosθ=cosθ

Simplify

2sinθ=cos^2θ

Recall the trignometric pythagora's rule:cos^2θ=1-sin^2θ

2sinθ=1-sin^2θ

sin^2θ+2sinθ-1=0

sinθ=-2+√4-(-4)/2

        =(-2+√8) /2

        =-1+√2

θ=24.456,155.544,