{"status": "success", "data": {"description_md": "**POTD February 25, 2024**\n\n$\\sum\\limits_{n=0}^\\infty\\frac{\\sin (nx)}{3^n}$, if $\\sin x=1/3$ and $0 \\leq x\\leq \\frac{\\pi}{2}$, can be written as $\\frac{a+b \\sqrt c}{d}$, where $c$ is a positive integer not divisible by the square of any prime and $a,b,c$ are positive integers such that $\\gcd (a,b,c)=1$. Find $a+b+c+d$.", "description_html": "<p><strong>POTD February 25, 2024</strong></p>&#10;<p><span class=\"katex--inline\">\\sum\\limits_{n=0}^\\infty\\frac{\\sin (nx)}{3^n}</span>, if <span class=\"katex--inline\">\\sin x=1/3</span> and <span class=\"katex--inline\">0 \\leq x\\leq \\frac{\\pi}{2}</span>, can be written as <span class=\"katex--inline\">\\frac{a+b \\sqrt c}{d}</span>, where <span class=\"katex--inline\">c</span> is a positive integer not divisible by the square of any prime and <span class=\"katex--inline\">a,b,c</span> are positive integers such that <span class=\"katex--inline\">\\gcd (a,b,c)=1</span>. Find <span class=\"katex--inline\">a+b+c+d</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #79", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}