If tan θ + cot θ = 2, and θ is an acute angle, then find the value of θ.

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Given tan θ + cot θ = 2.

Recall that cot θ = 1 / tan θ.

So, tan θ + 1 / tan θ = 2.

Let x = tan θ.

Then, x + 1/x = 2.

Multiply both sides by x:

x^2 + 1 = 2x

Rearranged:

x^2 - 2x + 1 = 0

This is (x - 1)^2 = 0

So, x = 1

Therefore, tan θ = 1.

For an acute angle θ, tan θ = 1 at θ = 45°.

Hence, the value of θ is 45°.

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