System of equations in a,b,c,d $a,b,c,d$ are complex numbers satisfying
\begin{cases}
  a+b+c+d=3 \\
  a^2+ b^2+ c^2+ d^2=5 \\
  a^3+ b^3+ c^3+ d^3=3 \\
  a^4+ b^4+ c^4+ d^4=9
\end{cases}
Find the value of the following: $$a^{2015} + b^{2015} + c^{2015} + d^{2015}$$.

Hint
Let $a_{n}=a^n+b^n+c^n+d^n$,then 
$$a_{n+3}=(a+b+c+d)a_{n+2}-(ab+ac+ad+bc+bd+cd)a_{n+1}+(abc+abd+acd+bcd)a_{n}-abcd\cdot a_{n-1}$$
and you have only find this $ab+ac+ad+bc+bd+cd,abc+abd+acd+bcd,abcd$ this is not hard to find it
