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Geometry Level 3

sin2016(x)sin(x)(sin(x)+1)+(i=12016sini(x)cos2(x))=34\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(0,90)x\in(0,90^{\circ}). Enter the magnitude of your answer in degrees.


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Hey! I had my boards on the past month, and so I wasn't really active. I had a great time clearing all the 130130 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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