Precal- Trigonometry (please help)

Question

Part a: Use an Addition or Subtraction Formula to simplify the equation.

sin(2𝜃) cos(𝜃) − cos(2𝜃) sin(𝜃) = √2/2

Part b: Find all solutions in the interval [0, 2𝜋). (Enter your answers as a comma-separated list.)

𝜃=

Thank you so much!

Answer 1

Use sin(a-b) = sin(a)cos(b)-cos(a)sin(b)

sin(2θ)cos(θ)-cos(2θ)sin(θ) = sin(2θ-θ) = sin(θ) = √2/2

From unit circle for sin(θ) = √2/2 ,

θ = π/4, 3π/4