For real numbers $x$, let \[P(x)=1+\cos(x)+i \sin(x)-\cos(2x)-i \sin(2x)+\cos(3x)+i \sin(3x)\] where $i=\sqrt{-1}$. Find the number of values of $x$ with $0 \leq x<2 \pi$ such that $P(x)=0$.

Let's think step by step and output the final answer within \boxed{}.
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