Without using trigonometric table, the value of
`cotthetatan(90^(@)-theta)-sec(90^(@)-theta)"cosec"theta+sin^(2)65^(@)+sin^(2)25^(@)+sqrt3tan5^(@)tan85^(@)`.

Answer

To solve the expression

\[ \text{cottheta} \cdot \tan(90^\circ - \theta) - \sec(90^\circ - \theta) \cdot \csc \theta + \sin^2 65^\circ + \sin^2 25^\circ + \sqrt{3} \tan 5^\circ \tan 85^\circ, \]

we will break it down step by step.

### Step 1: Simplify the first part
The first part of the expression is

\[ \text{cottheta} \cdot \tan(90^\circ - \theta). \]

Using the trigonometric identity, we know that

\[ \tan(90^\circ - \theta) = \cot \theta. \]

Thus,

\[ \text{cottheta} \cdot \tan(90^\circ - \theta) = \cot \theta \cdot \cot \theta = \cot^2 \theta. \]

### Step 2: Simplify the second part
Next, we simplify

\[ -\sec(90^\circ - \theta) \cdot \csc \theta. \]

Using the identity, we have

\[ \sec(90^\circ - \theta) = \csc \theta. \]

Thus,

\[ -\sec(90^\circ - \theta) \cdot \csc \theta = -\csc \theta \cdot \csc \theta = -\csc^2 \theta. \]

### Step 3: Combine the first two parts
Now we can combine the results from Step 1 and Step 2:

\[ \cot^2 \theta - \csc^2 \theta. \]

Using the identity

\[ \csc^2 \theta - \cot^2 \theta = 1, \]

we can rearrange this to:

\[ \cot^2 \theta - \csc^2 \theta = -1. \]

### Step 4: Simplify the sine squares
Next, we simplify

\[ \sin^2 65^\circ + \sin^2 25^\circ. \]

Using the identity \(\sin^2 A + \sin^2 B = 1 - \frac{1}{2}(\cos(2A) + \cos(2B))\), we can compute:

\[ \sin^2 65^\circ + \sin^2 25^\circ = \sin^2 65^\circ + \cos^2 65^\circ = 1. \]

### Step 5: Simplify the tangent product
Now we simplify

\[ \sqrt{3} \tan 5^\circ \tan 85^\circ. \]

Using the identity \(\tan(90^\circ - \theta) = \cot \theta\), we have

\[ \tan 85^\circ = \cot 5^\circ. \]

Thus,

\[ \tan 5^\circ \tan 85^\circ = \tan 5^\circ \cdot \cot 5^\circ = 1. \]

Therefore,

\[ \sqrt{3} \tan 5^\circ \tan 85^\circ = \sqrt{3} \cdot 1 = \sqrt{3}. \]

### Step 6: Combine all parts
Now we can combine all parts of the expression:

\[ -1 + 1 + \sqrt{3} = \sqrt{3}. \]

Thus, the final answer is

\[ \sqrt{3}. \]