\(\text{If } a, b, c \text{ are positive real numbers such that } a^2 + b^2 + c^2 = 3 \text{, prove following inequality:}\) $$\frac{a^4+3ab^3}{a^3+2b^3} + \frac{b^4+3bc^3}{b^3+2c^3} + \frac{c^4+3ca^3}{c^3+2a^3} \leq 4.$$