hard and im confused

Question

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)

(tan² θ − 4)(2 cos θ + 1) = 0

θ =

 

Answer 1

Step 1:

The trigonometric equation is .

Factors the equation

Let .

Difference of squares formula: .

Substitute in the factor.

and .

General solution :

If , then , where is an integer.

Step 2:

General solution :

If , then , where is an integer.

Solution :

The general solution is .