2014 Singapore MO (Open Rd 1) Problem 16

2014 SMO (Open-Rd1) 16. Let ABC be a triangle with a = BC, b = AC, and c = AB. Assume that 3a^2 + 3b^2 = 5c^2. Find the value of

\displaystyle\frac{\cot A + \cot B}{\cot C}.

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