500 followers problem-1

Algebra Level 4

$\dfrac{1}{1+a^4}+\dfrac{1}{1+b^4}+\dfrac{1}{1+c^4}+\dfrac{1}{1+d^4}=1$

Let $a,b,c$ and $d$ be positive real numbers satisfying the equation above, find the minimum value of $abcd$ .