Answer
$$\sin^3\theta+\cos^3\theta+\sin\theta\cos^2\theta+\sin^2\theta\cos\theta=\sin\theta+\cos\theta$$
The details of explanation is in the Work step by step below.
Work Step by Step
$$\sin^3\theta+\cos^3\theta+\sin\theta\cos^2\theta+\sin^2\theta\cos\theta=\sin\theta+\cos\theta$$
Take a look at the left side.
$$X=\sin^3\theta+\cos^3\theta+\sin\theta\cos^2\theta+\sin^2\theta\cos\theta$$
$$X=(\sin^3\theta+\sin\theta+\cos^2\theta)+(\cos^3\theta+\sin^2\theta\cos\theta)$$
$$X=\sin\theta(\sin^2\theta+\cos^2\theta)+\cos\theta(\cos^2\theta+\sin^2\theta)$$
- Now we already see that $\sin^2\theta+\cos^2\theta$ can be written into $1$, as stated in Pythagorean Identities.
$$X=\sin\theta\times1+\cos\theta\times1$$
$$X=\sin\theta+\cos\theta$$
So, $$\sin^3\theta+\cos^3\theta+\sin\theta\cos^2\theta+\sin^2\theta\cos\theta=\sin\theta+\cos\theta$$
The equation is verified to be an identity now.
