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 \(abcd\).