{"status": "success", "data": {"description_md": "If $\\alpha, \\beta, \\gamma,$ are the $3$ angles of a triangle. $\\sin^2\\alpha + \\sin^2\\beta + \\sin^2\\gamma = 1$. If $\\cos\\alpha \\cdot \\cos\\beta \\cdot \\cos\\gamma$ can be represented as $-\\dfrac{m}{n}.$ Compute $m + n.$", "description_html": "<p>If <span class=\"katex--inline\">\\alpha, \\beta, \\gamma,</span> are the <span class=\"katex--inline\">3</span> angles of a triangle. <span class=\"katex--inline\">\\sin^2\\alpha + \\sin^2\\beta + \\sin^2\\gamma = 1</span>. If <span class=\"katex--inline\">\\cos\\alpha \\cdot \\cos\\beta \\cdot \\cos\\gamma</span> can be represented as <span class=\"katex--inline\">-\\dfrac{m}{n}.</span> Compute <span class=\"katex--inline\">m + n.</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "Christmas Contest - Guts Round - Set 8 Problem 3", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}