If \( f(x) \) and \( g(x) \) are functions such that \( f(x+y)=f(x)...

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If \( f(x) \) and \( g(x) \) are functions such that \( f(x+y)=f(x) \) \( g(y)+g(x) f(y) \), then \( \left|\begin{array}{lll}f(\alpha) & g(\alpha) & f(\alpha+\theta) \\ f(\beta) & g(\beta) & f(\beta+\theta) \\ f(\gamma) & g(\gamma) & f(\gamma+\theta)\end{array}\right| \) is independent of
(A) \( \alpha \)
(B) \( \beta \)
(C) \( \gamma \)
(D) \( \theta \)
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