Consider the function \( f(x) = a x^2 + b x \cos \theta + c \sin \theta \) where \( a, b, \) and \( c \) are constants. For what values of \(\theta\) in the interval \(0 \leq \theta \leq 2\pi\) does the inequality \( f(x) > 0 \) hold for all \( x \) in the interval \(0 \leq x \leq 1\)? Assume \( a, b, \) and \( c \) are such that \( f(x) \) is always positive for \( x \) in this interval. Let's think step by step and output the final answer within \boxed{}.
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