$$\sin(60+\theta)-\cos(30-\theta)=\sin60\cos\theta\ +\cos60\sin\theta\ -\left(\cos30\cos\theta\ +\sin30\sin\theta\ \right)$$
$$=\frac{\sqrt{3}}{2}\cos\theta\ +\frac{1}{2}\sin\theta\ -\left(\frac{\sqrt{3}}{2}\cos\theta\ +\frac{1}{2}\sin\theta\ \right)$$
$$=\frac{\sqrt{3}}{2}\cos\theta\ +\frac{1}{2}\sin\theta\ -\frac{\sqrt{3}}{2}\cos\theta\ -\frac{1}{2}\sin\theta\ $$
$$=0$$
Hence, the correct answer is Option C
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