{"status": "success", "data": {"description_md": "Let $f(\\theta) = (16\\cos^2(\\theta)-16\\cos^4(\\theta))(3-12\\sin^2(\\theta)+12\\sin^4(\\theta))$. If the value of $$\\sum\\limits_{n=1}^{6} f(3.75n^\\circ)$$ is $\\dfrac{a}{b}$, where $a$ and $b$ are relatively prime positive integers, find $10a+b$.", "description_html": "<p>Let <span class=\"katex--inline\">f(\\theta) = (16\\cos^2(\\theta)-16\\cos^4(\\theta))(3-12\\sin^2(\\theta)+12\\sin^4(\\theta))</span>. If the value of <span class=\"katex--display\">\\sum\\limits_{n=1}^{6} f(3.75n^\\circ)</span> is <span class=\"katex--inline\">\\dfrac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime positive integers, find <span class=\"katex--inline\">10a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "March Break 2024 - Problem 3", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}