Evaluate the definite integral ${\int }_0^3\sin (\theta )d\theta$ exactly, using the Fundamental Theorem, then evaluate the same integral approximately. NOTE: Round the approximate value to three decimal places.
Example: Exact value $=\ln (3\pi )$. Approximate value $=2.243$.
Exact value $=$
Approximate value $=$

Step 1 ：First, we need to find the antiderivative of the function $\sin (\theta )$, which is $-\cos (\theta )$.

Step 2 ：Next, we apply the Fundamental Theorem of Calculus, which states that the definite integral of a function from a to b is equal to the antiderivative evaluated at b minus the antiderivative evaluated at a. In this case, a is 0 and b is 3.

Step 3 ：So, we evaluate $-\cos (\theta )$ at $\theta =3$ and $\theta =0$, and subtract the two values.

Step 4 ：The exact value of the integral is thus $-\cos (3)-(-\cos (0))$, which is approximately 1.9899924966004454.

Step 5 ：For the approximate value, we can use numerical integration methods. The approximate value of the integral is also approximately 1.99.

Step 6 ：Final Answer: The exact value of the integral is $\boxed{{\displaystyle 1.99}}$ and the approximate value is also $\boxed{{\displaystyle 1.99}}$.