For questions 3 and 4, what values for theta (0 less than or equal to. theta. less than or equal to 2pi)

3. 3sin (theta) = sin (theta) - 1

A. pi/3, 5pi/3

B. 2pi/3, 4pi/3

C. pi/6, 3pi/6

D. 7pi/6, 11pi/6

4. tan^2 (theta) = - 3/2 sec (theta)

A. pi/2, 5pi/2

B. 3pi/4, 5pi/4

C. pi/3, 5pi/3

D. 2pi/3, 4pi/3

3.) 3sinθ = sinθ - 1

3sinθ - sinθ = - 1

2sinθ = - 1

sinθ = - 1/2

θ = sin^-1 (-1/2) = π + π/6, 2π - π/6 = 7π/6, 11π/6

4.) tan^2 θ = - 3/2 sec θ

sin^2 θ / cos^2 θ = - 3/2 (1/cos θ)

sin^2 θ / cos θ = - 3/2

1 - cos^2 θ = - 3/2 cos θ

cos^2 θ - 3/2 cos θ - 1 = 0

2cos^2 θ - 3cos θ - 2 = 0

2cos^2 θ - 4cos θ + cos θ - 2 = 0

2cos θ (cos θ - 2) + 1 (cos θ - 2) = 0

(2cos θ + 1) = 0 or (cos θ - 2) = 0

cos θ = - 1/2 or cos θ = 2 [but cos θ can never be 2]

θ = cos^-1 (-1/2) = π - π/3, π + π/3 = 2π/3, 4π/3