If vector b, c, d are non coplanar vectors then prove that the vector r=( aX b)X( c X d)+( aX c )X( dX b)+( aX d)X( bX c) must be parallel to vector a .

I try to solve this question by using vector triple product and at last i got

2[a, b, c] d +2[a, d, b] c+2[a, c,d] b

Where [a, b, c,] Shows scalar triple product and X means cross product. now what to do next .taking cross product with a it should give 0

But how?