\(f(\theta)=\sin \theta\) has a period of \(2\pi\) such that consecutive half-period values have the same absolute values but alternate in sign.

Since \(f(\theta+\pi)\) means the value of \(f(\theta)\) after a half-period, then we only take the opposite of its value:

\(f(\theta+\pi)= -0.2\)

Since \(f(\theta+\pi)\) means the value of \(f(\theta)\) after a half-period, then we only take the opposite of its value:

\(f(\theta+\pi)= -0.2\)