given 2sin(theta)cos(theta)+cos(theta)=0. Find Theta.?

Assume that 0° ≤ θ < 360°

2 sinθ cosθ + cosθ = 0
cosθ (2 sinθ + 1) = 0
cosθ = 0 or 2 sinθ + 1 = 0
cosθ = 0 or sinθ = -1/2
θ = 90° or θ = (180° + 30°), (360° - 30°)
θ = 90° , 210°, 330°

: give answers in degrees if
sin2 theta+cos theta=0
I am not sure how to start this problem other than sin2 theta would be
(2sin theta cos theta)

give answers in degrees if
sin2 theta+cos theta=0
====================================
You already recognized that you need to use the trig identity sin(2 theta)=2sin(theta)cos(theta)
Substituting that expression gives (and letting theta = x to make it easier to write):
2sin(x)cos(x)+cos(x)=0
cos(x)(2sin(x)+1)=0

This equation is satisfied if either of the two factors are equal to 0.
So we have
cos(x) = 0
2sin(x)+1 = 0
Restricting ourselves to the interval (0,360 deg) the two solutions are
x = 90 deg
sin(x) = -1/2
x = 210 deg

2sinθcosθ + cosθ = 0
cosθ(2sinθ + 1) = 0
cosθ=0 or sinθ = -1/2
θ = 90°, 270°, 210°, and 330° where 0° ≤ θ < 360°
Graph: https://www.desmos.com/calculator/khxlqaoq63

Incomplete question.