Verified answer

First, factor:

(sinθ - 4)(sinθ + 1) = 0

Now set each factor equal to zero and solve:

sinθ - 4 = 0

sinθ = 4

Since the sine function has a range [-1, 1], there is no solution from this factor. Let' try the 2nd factor:

sinθ + 1 = 0

sinθ = -1

The sine function is -1 at 270 degrees (3pi/2 radians) and whole circle multiples thereof:

θ = 3pi/2 + 2pi*k, where k is any integer

sin^2 θ - 3sinθ - 4 = 0

let be u = sinθ

then

u^2 - 3u - 4 = 0

u = -1 is an obvious solution, and the other is -(-4)/1 = 4

u = 4 is not suitable for the u = sinθ solution

so

the solutions are given for : sinθ = - 1

θ = - pi/2 + 2kpi where k is an integer

hope it' ll help !!