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For $$ 0^\circ < \theta < 90^\circ$$, $$tan\theta + cot\theta$$ = 2 is equal to:
If $$tan\theta + cot\theta$$ = 2
Then $$\tan\theta+\frac{1}{\tan\theta\ }=2$$
If the sum of a number and its reciprocal = 2
then the number is equal to 1
So, $$\tan\theta\ =1=45^{^{\circ\ }}$$
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