QPaperGen

We know that
\[
\sin\frac{\pi}{6} = \frac{1}{2}, \quad \cos\frac{\pi}{3} = \frac{1}{2}, \quad \tan\frac{\pi}{4} = 1.
\]

Substituting these values:
\[
\sin^2\frac{\pi}{6} + \cos^2\frac{\pi}{3} - \tan^2\frac{\pi}{4}
= \left(\frac{1}{2}\right)^2 + \left(\frac{1}{2}\right)^2 - (1)^2
\]

\[
= \frac{1}{4} + \frac{1}{4} - 1
= \frac{1}{2} - 1 = -\frac{1}{2}.
\]