1. The problem asks us to find the value of $\tan \frac{\pi}{4}$.\n\n2. Recall that $\frac{\pi}{4}$ radians is equivalent to 45 degrees.\n\n3. The tangent of 45 degrees (or $\frac{\pi}{4}$ radians) is known to be 1, because tangent is the ratio of the opposite side to the adjacent side in a right triangle, and at 45 degrees both sides are equal.\n\n4. Therefore,\n$$\tan \frac{\pi}{4} = 1.$$\n\nFinal answer: 1.