Find the exact value of $\arctan \left(\tan \left(-\frac{\pi}{4}\right)\right)$
Write your answer in radians in terms of $\pi$.

Step 1 ：We are given \(\tan\left(-\frac{\pi}{4}\right)\)

Step 2 ：Using the periodicity of the tangent function, we can rewrite it as \(\tan\left(-\frac{\pi}{4} + \pi\right)\)

Step 3 ：Simplifying the angle inside the tangent function, we have \(\tan\left(\frac{3\pi}{4}\right)\)

Step 4 ：Using the property of the tangent function, we can express it as \(\frac{\sin\left(\frac{3\pi}{4}\right)}{\cos\left(\frac{3\pi}{4}\right)}\)

Step 5 ：At \(\frac{3\pi}{4}\), the sine function is \(\frac{\sqrt{2}}{2}\) and the cosine function is \(-\frac{\sqrt{2}}{2}\)

Step 6 ：Therefore, \(\tan\left(\frac{3\pi}{4}\right) = -1\)

Step 7 ：Taking the inverse tangent of \(-1\), we get the exact value of \(\arctan\left(\tan\left(-\frac{\pi}{4}\right)\right)\)

Step 8 ：Since \(-1\) corresponds to an angle of \(-\frac{\pi}{4}\), the final answer is \(\boxed{-\frac{\pi}{4}}\)