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Recently, I met one problem about matrix.

The problem is as follow:

Show that the matrix below has NO non-trivial solution if a+b+c=0

The matrix is

1 cos(c) cos(b)

cos(c) 1 cos(a)

cos(b) cos(a) 1

With the highlighted word 'NO', is it means that the only solution to the matrix is [0]?

If it is so, I would have to find the determinant of the matrix, right?

But still I find that the working was rather complicated with the trigonometric function as the element of the matrix.

So, can someone help me to solve this problem?

I appreciate those who offers help to me^^

Thank you very much to all of you!!!