`(sin^(2) 20^(@) + sin^(2) 70^(@))/(cos^(2) 20^(@) + cos^(2) 70^(@)) + [ (sin (90^(@) - theta).sin theta)/(tan theta) + (cos (90^(@) - theta).cos theta)/(cot theta) ]`.

Answer

To solve the given expression step by step, we will break it down into manageable parts.

### Given Expression:
\[ \frac{\sin^2 20^\circ + \sin^2 70^\circ}{\cos^2 20^\circ + \cos^2 70^\circ} + \left( \frac{\sin(90^\circ - \theta) \cdot \sin \theta}{\tan \theta} + \frac{\cos(90^\circ - \theta) \cdot \cos \theta}{\cot \theta} \right) \]

### Step 1: Simplify the first part of the expression
Using the complementary angle identity:
\[ \sin(90^\circ - x) = \cos x \quad \text{and} \quad \cos(90^\circ - x) = \sin x \]
We can rewrite \(\sin^2 70^\circ\) and \(\cos^2 70^\circ\):
\[ \sin^2 70^\circ = \sin^2(90^\circ - 20^\circ) = \cos^2 20^\circ \]
\[ \cos^2 70^\circ = \cos^2(90^\circ - 20^\circ) = \sin^2 20^\circ \]

Thus, we can substitute these into our expression:
\[ \frac{\sin^2 20^\circ + \cos^2 20^\circ}{\cos^2 20^\circ + \sin^2 20^\circ} \]

### Step 2: Apply the Pythagorean Identity
Using the Pythagorean identity:
\[ \sin^2 x + \cos^2 x = 1 \]
We can simplify:
\[ \frac{1}{1} = 1 \]

### Step 3: Simplify the second part of the expression
Now, we simplify the second part:
\[ \frac{\sin(90^\circ - \theta) \cdot \sin \theta}{\tan \theta} + \frac{\cos(90^\circ - \theta) \cdot \cos \theta}{\cot \theta} \]
Using the complementary angle identities again:
\[ \sin(90^\circ - \theta) = \cos \theta \quad \text{and} \quad \cos(90^\circ - \theta) = \sin \theta \]
Substituting these in:
\[ \frac{\cos \theta \cdot \sin \theta}{\tan \theta} + \frac{\sin \theta \cdot \cos \theta}{\cot \theta} \]

### Step 4: Rewrite \(\tan\) and \(\cot\)
Recall that:
\[ \tan \theta = \frac{\sin \theta}{\cos \theta} \quad \text{and} \quad \cot \theta = \frac{\cos \theta}{\sin \theta} \]
Thus:
\[ \frac{\cos \theta \cdot \sin \theta}{\frac{\sin \theta}{\cos \theta}} + \frac{\sin \theta \cdot \cos \theta}{\frac{\cos \theta}{\sin \theta}} \]
This simplifies to:
\[ \cos^2 \theta + \sin^2 \theta \]

### Step 5: Apply the Pythagorean Identity Again
Using the Pythagorean identity again:
\[ \cos^2 \theta + \sin^2 \theta = 1 \]

### Step 6: Combine the results
Now we combine the results from Step 2 and Step 5:
\[ 1 + 1 = 2 \]

### Final Answer:
Thus, the value of the entire expression is:
\[ \boxed{2} \]