Let `alpha` be a real number such that `0 <= alpha <= pi.` If `f(x)=cosx+cos(x+alpha)+cos(x+2alpha)` takes some constant number c for any `x in R,` then the value of `[c + alpha]` is equal to (Note : [y] denotes greatest integer less than or equal to y.)

Explanation

To solve the problem, we need to analyze the function \( f(x) = \cos x + \cos(x + \alpha) + \cos(x + 2\alpha) \) and determine the conditions under which it takes a constant value \( c \) for all \( x \in \mathbb{R} \).

### Step 1: Set up the function
We have:
\[ f(x) = \cos x + \cos(x + \alpha) + \cos(x + 2\alpha) \]

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