RU-SPB 2017 Problem 113

Given real numbers $x,y,z,t\in (0,\pi /2]$ such that $$\cos^2 (x)+\cos^2 (y) +\cos^2 (z) +\cos^2 (t)=1.$$ What is the minimum possible value of $$\cot (x) +\cot (y) +\cot (z) +\cot (t)?$$