Answer
$$\theta=15^\circ$$ satisfies what has been given.
Work Step by Step
$$\tan\theta=\cot(45^\circ+2\theta)$$
From the identity of the cofunction, we have $$\tan\theta=\cot(90^\circ-\theta)$$
Therefore, compared with what we have been given, we can deduce that $$\cot(45^\circ+2\theta)=\cot(90^\circ-\theta)$$ $$45^\circ+2\theta=90^\circ-\theta$$ $$3\theta=45^\circ$$ $$\theta=15^\circ$$
