1. **State the problem:** Given the equation $$\frac{\sin \theta + \cos \theta}{\sin \theta - \cos \theta} = 7,$$ find the value of $$\tan \theta.$$\n\n2. **Recall the formula and identities:** We know that $$\tan \theta = \frac{\sin \theta}{\cos \theta}.$$ We want to express the given equation in terms of $$\tan \theta$$ to solve for it.\n\n3. **Rewrite the given equation:** Let $$t = \tan \theta = \frac{\sin \theta}{\cos \theta}.$$ Then, $$\sin \theta = t \cos \theta.$$ Substitute into the numerator and denominator:\n$$\frac{\sin \theta + \cos \theta}{\sin \theta - \cos \theta} = \frac{t \cos \theta + \cos \theta}{t \cos \theta - \cos \theta} = \frac{\cos \theta (t + 1)}{\cos \theta (t - 1)}.$$\nSince $$\cos \theta \neq 0,$$ this simplifies to:\n$$\frac{t + 1}{t - 1} = 7.$$\n\n4. **Solve for $$t$$:**\nMultiply both sides by $$t - 1$$:\n$$t + 1 = 7(t - 1)$$\n$$t + 1 = 7t - 7$$\nBring all terms to one side:\n$$1 + 7 = 7t - t$$\n$$8 = 6t$$\nDivide both sides by 6:\n$$t = \frac{8}{6} = \frac{4}{3}.$$\n\n5. **Final answer:**\n$$\boxed{\tan \theta = \frac{4}{3}}.$$