2015 Trig

Geometry Level 4

In \( \bigtriangleup ABC \), the opposite sides of \( \angle A \), \( \angle B \), \( \angle C \) are \( a \), \( b \), \( c \) respectively. If \( a^{2}+b^{2}=tc^{2} \), and \( \cot C=2015( \cot A+\cot B) \), find the value of the constant \( t \).

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