### Home > PC3 > Chapter 8 > Lesson 8.3.3 > Problem8-117

8-117.

Yuka is trying to solve the following equation for $θ$, but is so confused by all the symbols; she does not know what to do.

$\frac{\sin^3(\theta)-4\sin(\theta)}{\sin^2(\theta)}=3$

1. Her friend Carlo suggests that she make the substitution $u = \sin\left(θ\right)$. Make this substitution and write the equation in terms of $u$.

2. Solve the equation for $u$.

Note: $u ≠ 0$ because you would have division by zero.
$u^{2} − 4u = 3u^{2}$
$u^{3} − 3u^{2} − 4u = 0$
$u\left(u^{2} − 3u − 4\right) = 0$

3. Solve the equation for $θ$ if $0 ≤ θ < 2π$.