$$(\sin \theta + \cos \theta)^2 = 2, 0^\circ < \theta < 90^\circ$$ then the value of $$\theta$$ is:

Given,   $$0^\circ < \theta < 90^\circ$$

$$=$$>  $$0^{\circ}<2\theta<180^{\circ}$$

$$(\sin \theta + \cos \theta)^2 = 2$$

$$=$$>  $$\sin^2\theta\ +\cos^2\theta\ +2\sin\theta\ \cos\theta\ =2$$

$$=$$>  $$1+2\sin\theta\ \cos\theta\ =2$$

$$=$$>  $$2\sin\theta\ \cos\theta\ =2-1$$

$$=$$>  $$\sin2\theta\ =1$$

$$=$$>  $$\sin2\theta\ =\sin\left(\frac{\pi\ }{2}\right)$$  since $$0^{\circ}<2\theta<180^{\circ}$$

$$=$$>  $$2\theta\ =\frac{\pi\ }{2}$$

$$=$$>  $$\theta\ =\frac{\pi\ }{4}$$

Hence, the correct answer is Option C