Let's find the value of \(sin^2 θ - cos^2 θ\) given that \(tan θ = 4/3\). We know that \(tan θ = sin θ / cos θ\), so if \(tan θ = 4/3\), then \(sin θ / cos θ = 4/3\). Cross-multiplying, we get \(3 sin θ = 4 cos θ\), or \(sin θ = (4/3) cos θ\). Squaring both sides, we get \(sin^2 θ = (16/9) cos^2 θ\).

Substituting this value of \(sin^2 θ\) into the expression for \(sin^2 θ - cos^2 θ\), we get:

\(sin^2 θ - cos^2 θ = (16/9) cos^2 θ - cos^2 θ\)

\(= (16/9 - 1) cos^2 θ\)

\(= (7/9) cos^2 θ\)

We can use the Pythagorean identity, \(sin^2 θ + cos^2 θ = 1\), to find the value of \(cos^2 θ\). Substituting the value of \(sin^2 θ\) that we found earlier, we get:

\((16/9) cos^2 θ + cos^2 θ = 1\)

\((25/9) cos^2 θ = 1\)

\(cos^2 θ = 9/25\)

Substituting this value of \(cos^2 θ\) into the expression for \(sin^2 θ - cos^2 θ\) that we found earlier, we get:

\(sin^2 θ - cos^2 θ = (7/9) cos^2 θ\)

\(= (7/9)(9/25)\)

\(= 7/25\)

So, if \(tan θ = 4/3\), then the value of \(sin^2θ - cos^2θ\) is 7/25