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Geometry Level 3

\[\sin^{2016}(x)\cdot\sin(x)\cdot(\sin(x)+1)+\left(\displaystyle\sum_{i=1}^{2016}\sin^{i}(x)\cos^{2}(x)\right)=\frac{3}{4}\]

Solve the equation above for \(x\in(0,90^{\circ})\). Enter the magnitude of your answer in degrees.


No need to read all of this.

Hey! I had my boards on the past month, and so I wasn't really active. I had a great time clearing all the \(130\) notifications I got. I now plan on being much more active on Brilliant than I used to be. So, yeah. Also, I put in a lot of time in making this problem. So tell me what you think about it! I'm open to all your suggestion and comments and criticism. Thanks!

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