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 \(\boxed{1.99}\) and the approximate value is also \(\boxed{1.99}\).