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Select the Scissors Tool and cut out the overlapping parts. Locate spot and click to cut it out. Then select the cut part and hit Delete.
Do the same with remaining pieces.
Fill the remaining gaps.
Select the outline shape and copy it (Ctrl + C). Press Ctrl + F (Paste Front). Select the Gradient Mesh Tool and click inside the cloud shape. This will add mesh lines.
Select the mesh points using the Mesh Tool and select a color from the color palette. After adding color send the shape backward ( Ctrl + Shift + [ )
Select all the shapes and copy them. Head back to Photoshop and paste it as a vector smart object.
Add dripping paint (drips and spray paint, 33.png)
Place it beneath the triangle shape layer.
Apply color overlay.
Switch back to Illustrator for one last time. Create the pattern in the following image. Use the Rectangle Tool to create the shape.
Select all the boxes and skew them using the Transform palette. (Window > Transform)
Copy and paste the shape in the main file.
Rotate the pattern by -60 degrees.
Place it beneath the base shapes. Resize it.
Add layer mask to the pattern. Set the foreground color to black. Load the grunge brushes set into the brushes palette. Select a grunge brush and place it over the pattern, and click to apply the brush. Make sure you apply the brush in the Layer Mask.
Open the Auto shapes palette. And choose the pattern below. Draw the pattern.
Make a circular selection above the pattern. Use the selection to add Layer Mask.
Here I applied a brush stroke using a grunge brush (Download link provided in resources).
Place this layer Just above the shape layer. Press Ctrl + Alt + G to clip it to the shape layer.
Add some nice highlights using a round soft brush. Then set the blending mode to Screen.
Let's create a light streak using the Brush Tool. Create a new layer. Click on the edge of the canvas.
Press Ctrl + T and stretch it vertically.
Lock the transparent pixels of the layer. Pick a nice foreground color and press Alt + Backspace to fill the color.