To solve for \( B \) in the expression provided, we will calculate each component step by step.

1. **Calculate \( \tan 24^\circ \) and \( \tan 66^\circ \)**:
\[
\tan 24^\circ \approx 0.4452
\]
\[
\tan 66^\circ \approx 2.246
\]

Now, multiply them:
\[
\tan 24^\circ \cdot \tan 66^\circ \approx 0.4452 \cdot 2.246 \approx 1.0001 \quad (\text{approximately } 1)
\]

2. **Calculate \( \sin^2 62^\circ \)**:
\[
\sin 62^\circ \approx 0.8746 \quad \Rightarrow \quad \sin^2 62^\circ \approx (0.8746)^2 \approx 0.7653
\]

3. **Calculate \( 3 \sin 31^\circ \)**:
\[
\sin 31^\circ \approx 0.5150
\]
\[
3 \sin 31^\circ \approx 3 \cdot 0.5150 \approx 1.545
\]

4. **Calculate \( 2 \cos 59^\circ \)**:
\[
\cos 59^\circ \approx 0.5150 \quad \Rightarrow \quad 2 \cos 59^\circ \approx 2 \cdot 0.5150 \approx 1.030
\]

5. **Calculate \( \cos^2 28^\circ \)**:
\[
\cos 28^\circ \approx 0.8829 \quad \Rightarrow \quad \cos^2 28^\circ \approx (0.8829)^2 \approx 0.778
\]

Now, substituting back into the equation:

### Putting it together

Now compute:
\[
B = (1 - 0.7653 - 1.545) / (1.030 + 0.778)
\]

Calculating the numerator:
\[
1 - 0.7653 - 1.545 \approx 1 - 2.3103 \approx -1.3103
\]

Calculating the denominator:
\[
1.030 + 0.778 \approx 1.808
\]

Thus, we have:
\[
B \approx \frac{-1.3103}{1.808} \approx -0.726
\]

So the final result for \( B \) is approximately:
\[
\boxed{-0.726}
\]