If the function \( f(x) = \mu \sin x + \frac{1}{3} \sin 3x \) has its derivative equal to zero at \( x = \frac{\pi}{3} \), then the value of \( \mu \) is __________.
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While differentiating \( \sin(ax) \), remember derivative becomes \( a\cos(ax) \)This cancels coefficients nicely in such problems.