https://file.aiquickdraw.com/mathbot/file/1728579121636sqsiyshb.jpg

The equation provided in the image is:

\[
4 \sin^5 \theta + \sin 5\theta = 0
\]

We are asked to find all the solutions for \(\theta\) in the interval \(0 \leq \theta \leq 2\pi\).

### Step 1: Simplifying the Equation

Factor out \(\sin \theta\):

\[
\sin \theta \left( 4 \sin^4 \theta + \cos 5\theta \right) = 0
\]

The equation is now factored into two parts:

1. \(\sin \theta = 0\)
2. \(4 \sin^x.

Find all the solutions of the equation 4sin^5(θ) + sin(5θ) = 0 which lie in the interval 0 ≤ θ ≤ 2π.

Learn how to solve the trigonometric equation 4sin^5(θ) + sin(5θ) = 0 in the interval 0 ≤ θ ≤ 2π. This problem covers important trigonometric concepts and equation solving, suitable for students in Grades 11-12.

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