{"status": "success", "data": {"description_md": "**POTD June 3, 2024**\n\nIf\n$$\\Large\\sum\\limits_{z=1}^{13}\\left[\\dfrac{1}{\\sin\\left(\\frac{\\pi}{4} + \\frac{(z-1)\\pi}{6}\\right)\\cdot\\sin(\\frac{\\pi}{4} + \\frac{z\\pi}{6})}\\right] $$\n\nCan be expressed as $a\\sqrt{b}-c$, where $a, b, c \\in \\mathbb{Z}^+$, and $b$ can not be divided by the square of any prime, find $abc$.", "description_html": "<p><strong>POTD June 3, 2024</strong></p>&#10;<p>If<br/>&#10;<span class=\"katex--display\">\\Large\\sum\\limits_{z=1}^{13}\\left[\\dfrac{1}{\\sin\\left(\\frac{\\pi}{4} + \\frac{(z-1)\\pi}{6}\\right)\\cdot\\sin(\\frac{\\pi}{4} + \\frac{z\\pi}{6})}\\right]</span></p>&#10;<p>Can be expressed as <span class=\"katex--inline\">a\\sqrt{b}-c</span>, where <span class=\"katex--inline\">a, b, c \\in \\mathbb{Z}^+</span>, and <span class=\"katex--inline\">b</span> can not be divided by the square of any prime, find <span class=\"katex--inline\">abc</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #176", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}