= Solution
Here $\deg K_C=2$. For $D$, $D-P$ and $D-P-Q$, including $Q=P$, the degrees are $5,4,3$, all greater than two. Thus the correction term in the <Riemann-Roch theorem> vanishes and
$$
\ell(D)=4,\qquad\ell(D-P)=3,\qquad\ell(D-P-Q)=2.
$$
The first drop supplies a section nonzero at every chosen point, proving <base-point-freeness of a linear system>. For distinct $P,Q$, the second drop supplies a section vanishing at one but not the other, proving point separation. For $Q=P$, it supplies a section vanishing to order exactly one, proving tangent separation. Hence the complete <linear system of divisors> is <very ample> and $\boxed{C\hookrightarrow\mathbb P^3}$ is the induced <closed immersion>.
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