{"status": "success", "data": {"description_md": "There are $2n$ complex numbers that satisfy both $z^{28}-z^{8}-1=0$ and $|z|=1$. These numbers have the form $z_{m}=\\cos\\theta_{m}+i\\sin\\theta_{m}$, where $0\\leq\\theta_{1}<\\theta_{2}< \\ldots <\\theta_{2n}<360$ and angles are measured in degrees. Find the value of $\\theta_{2}+\\theta_{4}+\\ldots+\\theta_{2n}$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>There are <span class=\"katex--inline\">2n</span> complex numbers that satisfy both <span class=\"katex--inline\">z^{28}-z^{8}-1=0</span> and <span class=\"katex--inline\">|z|=1</span>. These numbers have the form <span class=\"katex--inline\">z_{m}=\\cos\\theta_{m}+i\\sin\\theta_{m}</span>, where <span class=\"katex--inline\">0\\leq\\theta_{1}&lt;\\theta_{2}&lt; \\ldots &lt;\\theta_{2n}&lt;360</span> and angles are measured in degrees. Find the value of <span class=\"katex--inline\">\\theta_{2}+\\theta_{4}+\\ldots+\\theta_{2n}</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2001 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/01_aime_II_p15", "prev": "/problem/01_aime_II_p13"}}